proconlib

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:heavy_check_mark: tests/persistent_lazy_segtree/prod_apply_and_rollback.test.cpp

Depends on

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/persistent_range_affine_range_sum

#include <iostream>
#include <utility>
#include <vector>
#include "atcoder/modint.hpp"
#include "tools/persistent_lazy_segtree.hpp"

using mint = atcoder::modint998244353;

struct SM {
  using T = std::pair<int, mint>;
  static T op(const T& x, const T& y) {
    return {x.first + y.first, x.second + y.second};
  }
  static T e() {
    return {0, mint::raw(0)};
  }
};
using S = typename SM::T;

struct FM {
  using T = std::pair<mint, mint>;
  static T op(const T& f, const T& g) {
    return {f.first * g.first, f.first * g.second + f.second};
  }
  static T e() {
    return {mint::raw(1), mint::raw(0)};
  }
};
using F = typename FM::T;

S mapping(const F& f, const S& e) {
  return {e.first, f.first * e.second + f.second * mint::raw(e.first)};
}

int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);

  int N, Q;
  std::cin >> N >> Q;

  tools::persistent_lazy_segtree<SM, FM, mapping>::buffer buffer;
  std::vector<tools::persistent_lazy_segtree<SM, FM, mapping>> A_buffer(Q + 1);
  auto A = A_buffer.begin() + 1;
  A[-1] = tools::persistent_lazy_segtree<SM, FM, mapping>(buffer, [&]() {
    std::vector<S> a(N);
    for (auto& a_i : a) {
      int x;
      std::cin >> x;
      a_i = {1, mint::raw(x)};
    }
    return a;
  }());

  for (int q = 0; q < Q; ++q) {
    int t;
    std::cin >> t;
    if (t == 0) {
      int k, l, r, b, c;
      std::cin >> k >> l >> r >> b >> c;
      A[q] = A[k].apply(l, r, {mint::raw(b), mint::raw(c)});
    } else if (t == 1) {
      int k, s, l, r;
      std::cin >> k >> s >> l >> r;
      A[q] = A[k].rollback(A[s], l, r);
    } else {
      int k, l, r;
      std::cin >> k >> l >> r;
      std::cout << A[k].prod(l, r).second.val() << '\n';
    }
  }

  return 0;
}

#line 1 "tests/persistent_lazy_segtree/prod_apply_and_rollback.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/persistent_range_affine_range_sum

#include <iostream>
#include <utility>
#include <vector>
#line 1 "lib/ac-library/atcoder/modint.hpp"



#include <cassert>
#include <numeric>
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif

#line 1 "lib/ac-library/atcoder/internal_math.hpp"



#line 5 "lib/ac-library/atcoder/internal_math.hpp"

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;

    // @param m `1 <= m`
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned long long y = x * _m;
        return (unsigned int)(z - y + (z < y ? _m : 0));
    }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder


#line 1 "lib/ac-library/atcoder/internal_type_traits.hpp"



#line 7 "lib/ac-library/atcoder/internal_type_traits.hpp"

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder


#line 14 "lib/ac-library/atcoder/modint.hpp"

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder


#line 1 "tools/persistent_lazy_segtree.hpp"



#include <algorithm>
#include <array>
#line 7 "tools/persistent_lazy_segtree.hpp"
#include <functional>
#line 9 "tools/persistent_lazy_segtree.hpp"
#include <ranges>
#line 1 "tools/ceil_log2.hpp"



#line 1 "tools/bit_width.hpp"



#include <bit>
#line 1 "tools/is_integral.hpp"



#line 5 "tools/is_integral.hpp"

namespace tools {
  template <typename T>
  struct is_integral : ::std::is_integral<T> {};

  template <typename T>
  inline constexpr bool is_integral_v = ::tools::is_integral<T>::value;
}


#line 1 "tools/is_signed.hpp"



#line 5 "tools/is_signed.hpp"

namespace tools {
  template <typename T>
  struct is_signed : ::std::is_signed<T> {};

  template <typename T>
  inline constexpr bool is_signed_v = ::tools::is_signed<T>::value;
}


#line 1 "tools/make_unsigned.hpp"



#line 5 "tools/make_unsigned.hpp"

namespace tools {
  template <typename T>
  struct make_unsigned : ::std::make_unsigned<T> {};

  template <typename T>
  using make_unsigned_t = typename ::tools::make_unsigned<T>::type;
}


#line 10 "tools/bit_width.hpp"

namespace tools {
  template <typename T>
  constexpr int bit_width(T) noexcept;

  template <typename T>
  constexpr int bit_width(const T x) noexcept {
    static_assert(::tools::is_integral_v<T> && !::std::is_same_v<::std::remove_cv_t<T>, bool>);
    if constexpr (::tools::is_signed_v<T>) {
      assert(x >= 0);
      return ::tools::bit_width<::tools::make_unsigned_t<T>>(x);
    } else {
      return ::std::bit_width(x);
    }
  }
}


#line 6 "tools/ceil_log2.hpp"

namespace tools {
  template <typename T>
  constexpr T ceil_log2(T x) noexcept {
    assert(x > 0);
    return ::tools::bit_width(x - 1);
  }
}


#line 1 "tools/fix.hpp"



#line 6 "tools/fix.hpp"

namespace tools {
  template <typename F>
  struct fix : F {
    template <typename G>
    fix(G&& g) : F({::std::forward<G>(g)}) {
    }

    template <typename... Args>
    decltype(auto) operator()(Args&&... args) const {
      return F::operator()(*this, ::std::forward<Args>(args)...);
    }
  };

  template <typename F>
  fix(F&&) -> fix<::std::decay_t<F>>;
}


#line 15 "tools/persistent_lazy_segtree.hpp"

namespace tools {
  template <typename SM, typename FM, auto mapping>
  class persistent_lazy_segtree {
    using S = typename SM::T;
    using F = typename FM::T;
    static_assert(
      ::std::is_convertible_v<decltype(mapping), ::std::function<S(F, S)>>,
      "mapping must work as S(F, S)");

    struct node {
      S data;
      F lazy;
      ::std::array<int, 2> children;
    };

  public:
    class buffer {
      ::std::vector<::tools::persistent_lazy_segtree<SM, FM, mapping>::node> m_nodes;
      long long m_offset;
      long long m_size;
      int m_height;

    public:
      friend ::tools::persistent_lazy_segtree<SM, FM, mapping>;
    };

  private:
    ::tools::persistent_lazy_segtree<SM, FM, mapping>::buffer *m_buffer;
    int m_root;

    long long capacity() const {
      return 1LL << this->m_buffer->m_height;
    }

  public:
    persistent_lazy_segtree() = default;
    persistent_lazy_segtree(::tools::persistent_lazy_segtree<SM, FM, mapping>::buffer& buffer, const long long l_star, const long long r_star) :
      persistent_lazy_segtree(buffer, l_star, r_star, SM::e()) {
    }
    persistent_lazy_segtree(::tools::persistent_lazy_segtree<SM, FM, mapping>::buffer& buffer, const long long l_star, const long long r_star, const S& x) : m_buffer(&buffer) {
      assert(buffer.m_nodes.empty());
      assert(l_star <= r_star);
      buffer.m_offset = l_star;
      buffer.m_size = r_star - l_star;
      buffer.m_height = ::tools::ceil_log2(::std::max(1LL, r_star - l_star));
      buffer.m_nodes.push_back({x, FM::e(), {-1, -1}});
      for (int k = 1; k <= buffer.m_height; ++k) {
        buffer.m_nodes.push_back({SM::op(buffer.m_nodes.back().data, buffer.m_nodes.back().data), FM::e(), {k - 1, k - 1}});
      }
      this->m_root = buffer.m_height;
    }
    template <::std::ranges::range R>
    persistent_lazy_segtree(::tools::persistent_lazy_segtree<SM, FM, mapping>::buffer& buffer, R&& v) : m_buffer(&buffer) {
      assert(buffer.m_nodes.empty());
      for (auto&& x : v) {
        buffer.m_nodes.push_back({x, FM::e(), {-1, -1}});
      }
      buffer.m_offset = 0;
      buffer.m_size = buffer.m_nodes.size();
      buffer.m_height = ::tools::ceil_log2(::std::max(1LL, buffer.m_size));
      buffer.m_nodes.push_back({SM::e(), FM::e(), {-1, -1}});
      for (int h = 1; h <= buffer.m_height; ++h) {
        buffer.m_nodes.push_back({SM::e(), FM::e(), {static_cast<int>(buffer.m_nodes.size()) - 1, static_cast<int>(buffer.m_nodes.size()) - 1}});
      }
      this->m_root = ::tools::fix([&](auto&& dfs, const int h, const long long kl, const long long kr) -> int {
        assert(kl < kr);
        if (buffer.m_size <= kl) return buffer.m_size + h;
        if (h == 0) return kl;
        const auto km = ::std::midpoint(kl, kr);
        const auto left_child = dfs(h - 1, kl, km);
        const auto right_child = dfs(h - 1, km, kr);
        buffer.m_nodes.push_back({SM::op(buffer.m_nodes[left_child].data, buffer.m_nodes[right_child].data), FM::e(), {left_child, right_child}});
        return buffer.m_nodes.size() - 1;
      })(buffer.m_height, 0, this->capacity());
    }

    long long lower_bound() const {
      return this->m_buffer->m_offset;
    }
    long long upper_bound() const {
      return this->m_buffer->m_offset + this->m_buffer->m_size;
    }
    ::tools::persistent_lazy_segtree<SM, FM, mapping> set(long long p, const S& x) const {
      assert(this->lower_bound() <= p && p < this->upper_bound());
      auto& buffer = *this->m_buffer;
      p -= buffer.m_offset;

      auto res = *this;
      res.m_root = ::tools::fix([&](auto&& dfs, const int k, const long long kl, const long long kr, const F& lz) -> int {
        assert(kl < kr);
        if (p <= kl && kr <= p + 1) {
          buffer.m_nodes.push_back({x, FM::e(), buffer.m_nodes[k].children});
          return buffer.m_nodes.size() - 1;
        }
        if (kr <= p || p + 1 <= kl) {
          if (lz == FM::e()) return k;
          buffer.m_nodes.push_back({mapping(lz, buffer.m_nodes[k].data), FM::op(lz, buffer.m_nodes[k].lazy), buffer.m_nodes[k].children});
          return buffer.m_nodes.size() - 1;
        }
        const auto km = ::std::midpoint(kl, kr);
        const F next_lz = FM::op(lz, buffer.m_nodes[k].lazy);
        const auto left_child = dfs(buffer.m_nodes[k].children[0], kl, km, next_lz);
        const auto right_child = dfs(buffer.m_nodes[k].children[1], km, kr, next_lz);
        buffer.m_nodes.push_back({SM::op(buffer.m_nodes[left_child].data, buffer.m_nodes[right_child].data), FM::e(), {left_child, right_child}});
        return buffer.m_nodes.size() - 1;
      })(res.m_root, 0, res.capacity(), FM::e());
      return res;
    }
    S get(const long long p) const {
      return this->prod(p, p + 1);
    }
    S prod(long long l, long long r) const {
      assert(this->lower_bound() <= l && l <= r && r <= this->upper_bound());
      if (l == r) return SM::e();
      auto& buffer = *this->m_buffer;
      l -= buffer.m_offset;
      r -= buffer.m_offset;

      return ::tools::fix([&](auto&& dfs, const int k, const long long kl, const long long kr, const F& lz) -> S {
        assert(kl < kr);
        if (l <= kl && kr <= r) return mapping(lz, buffer.m_nodes[k].data);
        const auto km = ::std::midpoint(kl, kr);
        const F next_lz = FM::op(lz, buffer.m_nodes[k].lazy);
        S res = SM::e();
        if (l < km) res = SM::op(res, dfs(buffer.m_nodes[k].children[0], kl, km, next_lz));
        if (km < r) res = SM::op(res, dfs(buffer.m_nodes[k].children[1], km, kr, next_lz));
        return res;
      })(this->m_root, 0, this->capacity(), FM::e());
    }
    S all_prod() const {
      return this->m_buffer->m_nodes[this->m_root].data;
    }
    ::tools::persistent_lazy_segtree<SM, FM, mapping> apply(const long long p, const F& f) const {
      return this->apply(p, p + 1, f);
    }
    ::tools::persistent_lazy_segtree<SM, FM, mapping> apply(long long l, long long r, const F& f) const {
      assert(this->lower_bound() <= l && l <= r && r <= this->upper_bound());
      if (l == r) return *this;
      auto& buffer = *this->m_buffer;
      l -= buffer.m_offset;
      r -= buffer.m_offset;

      auto res = *this;
      res.m_root = ::tools::fix([&](auto&& dfs, const int k, const long long kl, const long long kr, const F& lz) -> int {
        assert(kl < kr);
        if (l <= kl && kr <= r) {
          const F modified_lz = FM::op(f, lz);
          buffer.m_nodes.push_back({mapping(modified_lz, buffer.m_nodes[k].data), FM::op(modified_lz, buffer.m_nodes[k].lazy), buffer.m_nodes[k].children});
          return buffer.m_nodes.size() - 1;
        }
        if (kr <= l || r <= kl) {
          if (lz == FM::e()) return k;
          buffer.m_nodes.push_back({mapping(lz, buffer.m_nodes[k].data), FM::op(lz, buffer.m_nodes[k].lazy), buffer.m_nodes[k].children});
          return buffer.m_nodes.size() - 1;
        }
        const auto km = ::std::midpoint(kl, kr);
        const F next_lz = FM::op(lz, buffer.m_nodes[k].lazy);
        const auto left_child = dfs(buffer.m_nodes[k].children[0], kl, km, next_lz);
        const auto right_child = dfs(buffer.m_nodes[k].children[1], km, kr, next_lz);
        buffer.m_nodes.push_back({SM::op(buffer.m_nodes[left_child].data, buffer.m_nodes[right_child].data), FM::e(), {left_child, right_child}});
        return buffer.m_nodes.size() - 1;
      })(res.m_root, 0, res.capacity(), FM::e());
      return res;
    }
    ::tools::persistent_lazy_segtree<SM, FM, mapping> rollback(const ::tools::persistent_lazy_segtree<SM, FM, mapping>& s, long long l, long long r) const {
      assert(this->m_buffer == s.m_buffer);
      assert(this->lower_bound() <= l && l <= r && r <= this->upper_bound());
      if (l == r) return *this;
      if (l == this->lower_bound() && r == this->upper_bound()) return s;
      auto& buffer = *this->m_buffer;
      l -= buffer.m_offset;
      r -= buffer.m_offset;

      auto res = *this;
      res.m_root = ::tools::fix([&](auto&& dfs, const int k1, const int k2, const long long kl, const long long kr, const F& lz1, const F& lz2) -> int {
        assert(kl < kr);
        if (l <= kl && kr <= r) {
          if (lz2 == FM::e()) return k2;
          buffer.m_nodes.push_back({mapping(lz2, buffer.m_nodes[k2].data), FM::op(lz2, buffer.m_nodes[k2].lazy), buffer.m_nodes[k2].children});
          return buffer.m_nodes.size() - 1;
        }
        if (kr <= l || r <= kl) {
          if (lz1 == FM::e()) return k1;
          buffer.m_nodes.push_back({mapping(lz1, buffer.m_nodes[k1].data), FM::op(lz1, buffer.m_nodes[k1].lazy), buffer.m_nodes[k1].children});
          return buffer.m_nodes.size() - 1;
        }
        const auto km = ::std::midpoint(kl, kr);
        const F next_lz1 = FM::op(lz1, buffer.m_nodes[k1].lazy);
        const F next_lz2 = FM::op(lz2, buffer.m_nodes[k2].lazy);
        const auto left_child = dfs(buffer.m_nodes[k1].children[0], buffer.m_nodes[k2].children[0], kl, km, next_lz1, next_lz2);
        const auto right_child = dfs(buffer.m_nodes[k1].children[1], buffer.m_nodes[k2].children[1], km, kr, next_lz1, next_lz2);
        buffer.m_nodes.push_back({SM::op(buffer.m_nodes[left_child].data, buffer.m_nodes[right_child].data), FM::e(), {left_child, right_child}});
        return buffer.m_nodes.size() - 1;
      })(res.m_root, s.m_root, 0, res.capacity(), FM::e(), FM::e());
      return res;
    }
    template <typename G>
    long long max_right(long long l, const G& g) const {
      assert(this->lower_bound() <= l && l <= this->upper_bound());
      assert(g(SM::e()));
      if (l == this->upper_bound()) return l;
      auto& buffer = *this->m_buffer;
      l -= buffer.m_offset;

      return buffer.m_offset + ::std::min(::tools::fix([&](auto&& dfs, const S& c, const int k, const long long kl, const long long kr, const F& lz) -> ::std::pair<S, long long> {
        assert(kl < kr);
        if (kl < l) {
          assert(kl < l && l < kr);
          const auto km = ::std::midpoint(kl, kr);
          const F next_lz = FM::op(lz, buffer.m_nodes[k].lazy);
          if (l < km) {
            const auto [hc, hr] = dfs(c, buffer.m_nodes[k].children[0], kl, km, next_lz);
            assert(l <= hr && hr <= km);
            if (hr < km) return {hc, hr};
            return dfs(hc, buffer.m_nodes[k].children[1], km, kr, next_lz);
          } else {
            return dfs(c, buffer.m_nodes[k].children[1], km, kr, next_lz);
          }
        } else {
          if (const auto wc = SM::op(c, mapping(lz, buffer.m_nodes[k].data)); g(wc)) return {wc, kr};
          if (kr - kl == 1) return {c, kl};
          const auto km = ::std::midpoint(kl, kr);
          const F next_lz = FM::op(lz, buffer.m_nodes[k].lazy);
          const auto [hc, hr] = dfs(c, buffer.m_nodes[k].children[0], kl, km, next_lz);
          assert(l <= hr && hr <= km);
          if (hr < km) return {hc, hr};
          return dfs(hc, buffer.m_nodes[k].children[1], km, kr, next_lz);
        }
      })(SM::e(), this->m_root, 0, this->capacity(), FM::e()).second, buffer.m_size);
    }
    template <typename G>
    long long min_left(long long r, const G& g) const {
      assert(this->lower_bound() <= r && r <= this->upper_bound());
      assert(g(SM::e()));
      if (r == this->lower_bound()) return r;
      auto& buffer = *this->m_buffer;
      r -= buffer.m_offset;

      return buffer.m_offset + ::tools::fix([&](auto&& dfs, const S& c, const int k, const long long kl, const long long kr, const F& lz) -> ::std::pair<S, long long> {
        assert(kl < kr);
        if (r < kr) {
          assert(kl < r && r < kr);
          const auto km = ::std::midpoint(kl, kr);
          const F next_lz = FM::op(lz, buffer.m_nodes[k].lazy);
          if (km < r) {
            const auto [hc, hl] = dfs(c, buffer.m_nodes[k].children[1], km, kr, next_lz);
            assert(km <= hl && hl <= r);
            if (km < hl) return {hc, hl};
            return dfs(hc, buffer.m_nodes[k].children[0], kl, km, next_lz);
          } else {
            return dfs(c, buffer.m_nodes[k].children[0], kl, km, next_lz);
          }
        } else {
          if (const auto wc = SM::op(mapping(lz, buffer.m_nodes[k].data), c); g(wc)) return {wc, kl};
          if (kr - kl == 1) return {c, kr};
          const auto km = ::std::midpoint(kl, kr);
          const F next_lz = FM::op(lz, buffer.m_nodes[k].lazy);
          const auto [hc, hl] = dfs(c, buffer.m_nodes[k].children[1], km, kr, next_lz);
          assert(km <= hl && hl <= r);
          if (km < hl) return {hc, hl};
          return dfs(hc, buffer.m_nodes[k].children[0], kl, km, next_lz);
        }
      })(SM::e(), this->m_root, 0, this->capacity(), FM::e()).second;
    }
  };
}


#line 8 "tests/persistent_lazy_segtree/prod_apply_and_rollback.test.cpp"

using mint = atcoder::modint998244353;

struct SM {
  using T = std::pair<int, mint>;
  static T op(const T& x, const T& y) {
    return {x.first + y.first, x.second + y.second};
  }
  static T e() {
    return {0, mint::raw(0)};
  }
};
using S = typename SM::T;

struct FM {
  using T = std::pair<mint, mint>;
  static T op(const T& f, const T& g) {
    return {f.first * g.first, f.first * g.second + f.second};
  }
  static T e() {
    return {mint::raw(1), mint::raw(0)};
  }
};
using F = typename FM::T;

S mapping(const F& f, const S& e) {
  return {e.first, f.first * e.second + f.second * mint::raw(e.first)};
}

int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);

  int N, Q;
  std::cin >> N >> Q;

  tools::persistent_lazy_segtree<SM, FM, mapping>::buffer buffer;
  std::vector<tools::persistent_lazy_segtree<SM, FM, mapping>> A_buffer(Q + 1);
  auto A = A_buffer.begin() + 1;
  A[-1] = tools::persistent_lazy_segtree<SM, FM, mapping>(buffer, [&]() {
    std::vector<S> a(N);
    for (auto& a_i : a) {
      int x;
      std::cin >> x;
      a_i = {1, mint::raw(x)};
    }
    return a;
  }());

  for (int q = 0; q < Q; ++q) {
    int t;
    std::cin >> t;
    if (t == 0) {
      int k, l, r, b, c;
      std::cin >> k >> l >> r >> b >> c;
      A[q] = A[k].apply(l, r, {mint::raw(b), mint::raw(c)});
    } else if (t == 1) {
      int k, s, l, r;
      std::cin >> k >> s >> l >> r;
      A[q] = A[k].rollback(A[s], l, r);
    } else {
      int k, l, r;
      std::cin >> k >> l >> r;
      std::cout << A[k].prod(l, r).second.val() << '\n';
    }
  }

  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++ example_00 :heavy_check_mark: AC 5 ms 4 MB
g++ example_01 :heavy_check_mark: AC 4 ms 4 MB
g++ max_less_query_types_00 :heavy_check_mark: AC 237 ms 203 MB
g++ max_less_query_types_01 :heavy_check_mark: AC 184 ms 104 MB
g++ max_less_query_types_02 :heavy_check_mark: AC 85 ms 12 MB
g++ max_less_query_types_03 :heavy_check_mark: AC 238 ms 203 MB
g++ max_less_query_types_04 :heavy_check_mark: AC 135 ms 56 MB
g++ max_less_query_types_05 :heavy_check_mark: AC 169 ms 105 MB
g++ max_random_00 :heavy_check_mark: AC 178 ms 103 MB
g++ max_random_01 :heavy_check_mark: AC 181 ms 105 MB
g++ max_random_02 :heavy_check_mark: AC 183 ms 105 MB
g++ random_00 :heavy_check_mark: AC 87 ms 55 MB
g++ random_01 :heavy_check_mark: AC 38 ms 30 MB
g++ random_02 :heavy_check_mark: AC 83 ms 55 MB
g++ small_00 :heavy_check_mark: AC 5 ms 4 MB
g++ small_01 :heavy_check_mark: AC 5 ms 4 MB
g++ small_02 :heavy_check_mark: AC 5 ms 4 MB
g++ small_03 :heavy_check_mark: AC 5 ms 4 MB
g++ small_04 :heavy_check_mark: AC 5 ms 4 MB
g++ small_05 :heavy_check_mark: AC 5 ms 4 MB
g++ small_06 :heavy_check_mark: AC 5 ms 4 MB
g++ small_07 :heavy_check_mark: AC 5 ms 4 MB
g++ small_08 :heavy_check_mark: AC 5 ms 4 MB
g++ small_09 :heavy_check_mark: AC 5 ms 4 MB
g++ small_random_00 :heavy_check_mark: AC 6 ms 4 MB
g++ small_random_01 :heavy_check_mark: AC 5 ms 4 MB
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