proconlib
This documentation is automatically generated by competitive-verifier/competitive-verifier
tests/has_mod.test.cpp
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- Last update: 2025-02-10 01:30:13+09:00
Depends on
- std::abs(x) extended for my library (tools/abs.hpp)
- Assertion macro (tools/assert_that.hpp)
- $\left\lceil \frac{x}{y} \right\rceil$ (tools/ceil.hpp)
- tools/detail/rolling_hash.hpp
- Extended Euclidean algorithm (tools/extgcd.hpp)
- Floyd's cycle-finding algorithm (tools/find_cycle.hpp)
- $\left\lfloor \frac{x}{y} \right\rfloor$ (tools/floor.hpp)
- std::gcd(m, n) extended for my library (tools/gcd.hpp)
- Check whether T has the member function mod() (tools/has_mod.hpp)
- std::is_integral extended for tools::int128_t and tools::uint128_t (tools/is_integral.hpp)
- Check whether T is a monoid (tools/is_monoid.hpp)
- std::is_unsigned extended for tools::int128_t and tools::uint128_t (tools/is_unsigned.hpp)
- Minimum non-negative reminder (tools/mod.hpp)
- $\mathbb{Z} / (2^{61} - 1) \mathbb{Z}$ (tools/modint_for_rolling_hash.hpp)
- Typical monoids (tools/monoid.hpp)
- The number of nanoseconds that have elapsed since epoch (tools/now.hpp)
- $b^n$ under a given monoid, and std::pow(b, n) extended for my library (tools/pow.hpp)
- Cache for $b^n \pmod{M}$ (tools/pow_mod_cache.hpp)
- $x^2$ under a given monoid (tools/square.hpp)
Code
// competitive-verifier: STANDALONE
#include <iostream>
#include <string>
#include "atcoder/modint.hpp"
#include "tools/assert_that.hpp"
#include "tools/has_mod.hpp"
#include "tools/modint_for_rolling_hash.hpp"
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
assert_that(!tools::has_mod_v<int>);
assert_that(!tools::has_mod_v<std::string>);
assert_that(tools::has_mod_v<atcoder::modint998244353>);
assert_that(tools::has_mod_v<atcoder::modint>);
assert_that(tools::has_mod_v<tools::modint_for_rolling_hash>);
assert_that(!tools::has_mod_v<std::vector<atcoder::modint998244353>>);
assert_that(!tools::has_mod_v<std::vector<atcoder::modint>>);
assert_that(!tools::has_mod_v<std::vector<tools::modint_for_rolling_hash>>);
return 0;
}
#line 1 "tests/has_mod.test.cpp"
// competitive-verifier: STANDALONE
#include <iostream>
#include <string>
#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"
#include <utility>
#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/assert_that.hpp"
#line 5 "tools/assert_that.hpp"
#include <cstdlib>
#define assert_that_impl(cond, file, line, func) do {\
if (!cond) {\
::std::cerr << file << ':' << line << ": " << func << ": Assertion `" << #cond << "' failed." << '\n';\
::std::exit(EXIT_FAILURE);\
}\
} while (false)
#define assert_that(...) assert_that_impl((__VA_ARGS__), __FILE__, __LINE__, __func__)
#line 1 "tools/has_mod.hpp"
#line 6 "tools/has_mod.hpp"
namespace tools {
template <typename T, typename = ::std::void_t<>>
struct has_mod : ::std::false_type {};
template <typename T>
struct has_mod<T, ::std::void_t<decltype(::std::declval<T>().mod())>> : ::std::true_type {};
template <typename T>
inline constexpr bool has_mod_v = ::tools::has_mod<T>::value;
}
#line 1 "tools/modint_for_rolling_hash.hpp"
#line 1 "tools/detail/rolling_hash.hpp"
#include <cstdint>
#line 6 "tools/detail/rolling_hash.hpp"
#include <tuple>
#include <vector>
#line 1 "tools/pow.hpp"
#line 6 "tools/pow.hpp"
#include <cmath>
#line 1 "tools/monoid.hpp"
#line 5 "tools/monoid.hpp"
#include <algorithm>
#include <limits>
#line 1 "tools/gcd.hpp"
#line 6 "tools/gcd.hpp"
namespace tools {
template <typename M, typename N>
constexpr ::std::common_type_t<M, N> gcd(const M m, const N n) {
return ::std::gcd(m, n);
}
}
#line 9 "tools/monoid.hpp"
namespace tools {
namespace monoid {
template <typename M, M ...dummy>
struct max;
template <typename M>
struct max<M> {
static_assert(::std::is_arithmetic_v<M>, "M must be a built-in arithmetic type.");
using T = M;
static T op(const T lhs, const T rhs) {
return ::std::max(lhs, rhs);
}
static T e() {
if constexpr (::std::is_integral_v<M>) {
return ::std::numeric_limits<M>::min();
} else {
return -::std::numeric_limits<M>::infinity();
}
}
};
template <typename M, M E>
struct max<M, E> {
static_assert(::std::is_integral_v<M>, "M must be a built-in integral type.");
using T = M;
static T op(const T lhs, const T rhs) {
assert(E <= lhs);
assert(E <= rhs);
return ::std::max(lhs, rhs);
}
static T e() {
return E;
}
};
template <typename M, M ...dummy>
struct min;
template <typename M>
struct min<M> {
static_assert(::std::is_arithmetic_v<M>, "M must be a built-in arithmetic type.");
using T = M;
static T op(const T lhs, const T rhs) {
return ::std::min(lhs, rhs);
}
static T e() {
if constexpr (::std::is_integral_v<M>) {
return ::std::numeric_limits<M>::max();
} else {
return ::std::numeric_limits<M>::infinity();
}
}
};
template <typename M, M E>
struct min<M, E> {
static_assert(::std::is_integral_v<M>, "M must be a built-in integral type.");
using T = M;
static T op(const T lhs, const T rhs) {
assert(lhs <= E);
assert(rhs <= E);
return ::std::min(lhs, rhs);
}
static T e() {
return E;
}
};
template <typename M>
struct multiplies {
private:
using VR = ::std::conditional_t<::std::is_arithmetic_v<M>, const M, const M&>;
public:
using T = M;
static T op(VR lhs, VR rhs) {
return lhs * rhs;
}
static T e() {
return T(1);
}
};
template <>
struct multiplies<bool> {
using T = bool;
static T op(const bool lhs, const bool rhs) {
return lhs && rhs;
}
static T e() {
return true;
}
};
template <typename M>
struct gcd {
private:
static_assert(!::std::is_arithmetic_v<M> || (::std::is_integral_v<M> && !::std::is_same_v<M, bool>), "If M is a built-in arithmetic type, it must be integral except for bool.");
using VR = ::std::conditional_t<::std::is_arithmetic_v<M>, const M, const M&>;
public:
using T = M;
static T op(VR lhs, VR rhs) {
return ::tools::gcd(lhs, rhs);
}
static T e() {
return T(0);
}
};
template <typename M, M E>
struct update {
static_assert(::std::is_integral_v<M>, "M must be a built-in integral type.");
using T = M;
static T op(const T lhs, const T rhs) {
return lhs == E ? rhs : lhs;
}
static T e() {
return E;
}
};
}
}
#line 1 "tools/square.hpp"
#line 1 "tools/is_monoid.hpp"
#line 6 "tools/is_monoid.hpp"
namespace tools {
template <typename M, typename = void>
struct is_monoid : ::std::false_type {};
template <typename M>
struct is_monoid<M, ::std::enable_if_t<
::std::is_same_v<typename M::T, decltype(M::op(::std::declval<typename M::T>(), ::std::declval<typename M::T>()))> &&
::std::is_same_v<typename M::T, decltype(M::e())>
, void>> : ::std::true_type {};
template <typename M>
inline constexpr bool is_monoid_v = ::tools::is_monoid<M>::value;
}
#line 6 "tools/square.hpp"
namespace tools {
template <typename M>
::std::enable_if_t<::tools::is_monoid_v<M>, typename M::T> square(const typename M::T& x) {
return M::op(x, x);
}
template <typename T>
::std::enable_if_t<!::tools::is_monoid_v<T>, T> square(const T& x) {
return x * x;
}
}
#line 9 "tools/pow.hpp"
namespace tools {
template <typename M, typename E>
::std::enable_if_t<::std::is_integral_v<E>, typename M::T> pow(const typename M::T& base, const E exponent) {
assert(exponent >= 0);
return exponent == 0
? M::e()
: exponent % 2 == 0
? ::tools::square<M>(::tools::pow<M>(base, exponent / 2))
: M::op(::tools::pow<M>(base, exponent - 1), base);
}
template <typename T, typename E>
::std::enable_if_t<::std::is_integral_v<E>, T> pow(const T& base, const E exponent) {
assert(exponent >= 0);
return ::tools::pow<::tools::monoid::multiplies<T>>(base, exponent);
}
template <typename T, typename E>
auto pow(const T base, const E exponent) -> ::std::enable_if_t<!::std::is_integral_v<E>, decltype(::std::pow(base, exponent))> {
return ::std::pow(base, exponent);
}
}
#line 1 "tools/extgcd.hpp"
#line 1 "tools/abs.hpp"
namespace tools {
constexpr float abs(const float x) {
return x < 0 ? -x : x;
}
constexpr double abs(const double x) {
return x < 0 ? -x : x;
}
constexpr long double abs(const long double x) {
return x < 0 ? -x : x;
}
constexpr int abs(const int x) {
return x < 0 ? -x : x;
}
constexpr long abs(const long x) {
return x < 0 ? -x : x;
}
constexpr long long abs(const long long x) {
return x < 0 ? -x : x;
}
constexpr unsigned int abs(const unsigned int x) {
return x;
}
constexpr unsigned long abs(const unsigned long x) {
return x;
}
constexpr unsigned long long abs(const unsigned long long x) {
return x;
}
}
#line 9 "tools/extgcd.hpp"
namespace tools {
template <typename T>
::std::tuple<T, T, T> extgcd(T prev_r, T r) {
const bool prev_r_is_neg = prev_r < T(0);
const bool r_is_neg = r < T(0);
if (prev_r_is_neg) prev_r = -prev_r;
if (r_is_neg) r = -r;
#ifndef NDEBUG
const T a = prev_r;
const T b = r;
#endif
T prev_s(1);
T prev_t(0);
T s(0);
T t(1);
while (r != T(0)) {
const T q = prev_r / r;
::std::tie(prev_r, r) = ::std::make_pair(r, prev_r - q * r);
::std::tie(prev_s, s) = ::std::make_pair(s, prev_s - q * s);
::std::tie(prev_t, t) = ::std::make_pair(t, prev_t - q * t);
}
if (prev_r_is_neg) prev_s = -prev_s;
if (r_is_neg) prev_t = -prev_t;
assert(::tools::abs(prev_s) <= ::std::max(b / prev_r / T(2), T(1)));
assert(::tools::abs(prev_t) <= ::std::max(a / prev_r / T(2), T(1)));
return ::std::make_tuple(prev_s, prev_t, prev_r);
}
}
#line 1 "tools/pow_mod_cache.hpp"
#line 5 "tools/pow_mod_cache.hpp"
#include <optional>
#line 8 "tools/pow_mod_cache.hpp"
#include <cstddef>
#line 10 "tools/pow_mod_cache.hpp"
#include <iterator>
#line 1 "tools/find_cycle.hpp"
#line 5 "tools/find_cycle.hpp"
namespace tools {
template <typename T, typename F>
::std::pair<long long, long long> find_cycle(const T& seed, const F& f) {
auto i = 1LL;
auto j = 2LL;
T x = f(seed);
T y = f(f(seed));
for (; x != y; ++i, j += 2, x = f(x), y = f(f(y)));
i = 0;
x = seed;
for (; x != y; ++i, ++j, x = f(x), y = f(y));
const auto head = i;
++i;
j = i + 1;
x = f(x);
y = f(f(y));
for (; x != y; ++i, j += 2, x = f(x), y = f(f(y)));
const auto cycle = j - i;
return ::std::make_pair(head, cycle);
}
}
#line 1 "tools/mod.hpp"
#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 7 "tools/mod.hpp"
namespace tools {
template <typename M, typename N> requires (
::tools::is_integral_v<M> && !::std::is_same_v<::std::remove_cv_t<M>, bool> &&
::tools::is_integral_v<N> && !::std::is_same_v<::std::remove_cv_t<N>, bool>)
constexpr ::std::common_type_t<M, N> mod(const M a, const N b) noexcept {
assert(b != 0);
using UM = ::std::make_unsigned_t<M>;
using UN = ::std::make_unsigned_t<N>;
const UM ua = a >= 0 ? a : static_cast<UM>(-(a + 1)) + 1;
const UN ub = b >= 0 ? b : static_cast<UN>(-(b + 1)) + 1;
auto r = ua % ub;
if (a < 0 && r > 0) {
r = ub - r;
}
return r;
}
}
#line 1 "tools/floor.hpp"
#line 7 "tools/floor.hpp"
namespace tools {
template <typename M, typename N> requires (
::tools::is_integral_v<M> && !::std::is_same_v<::std::remove_cv_t<M>, bool> &&
::tools::is_integral_v<N> && !::std::is_same_v<::std::remove_cv_t<N>, bool>)
constexpr ::std::common_type_t<M, N> floor(const M x, const N y) noexcept {
assert(y != 0);
if (y >= 0) {
if (x >= 0) {
return x / y;
} else {
return (x + 1) / y - 1;
}
} else {
if (x > 0) {
return (x - 1) / y - 1;
} else {
return x / y;
}
}
}
}
#line 1 "tools/ceil.hpp"
#line 1 "tools/is_unsigned.hpp"
#line 5 "tools/is_unsigned.hpp"
namespace tools {
template <typename T>
struct is_unsigned : ::std::is_unsigned<T> {};
template <typename T>
inline constexpr bool is_unsigned_v = ::tools::is_unsigned<T>::value;
}
#line 8 "tools/ceil.hpp"
namespace tools {
template <typename M, typename N> requires (
::tools::is_integral_v<M> && !::std::is_same_v<::std::remove_cv_t<M>, bool> &&
::tools::is_integral_v<N> && !::std::is_same_v<::std::remove_cv_t<N>, bool>)
constexpr ::std::common_type_t<M, N> ceil(const M x, const N y) noexcept {
assert(y != 0);
if (y >= 0) {
if (x > 0) {
return (x - 1) / y + 1;
} else {
if constexpr (::tools::is_unsigned_v<::std::common_type_t<M, N>>) {
return 0;
} else {
return x / y;
}
}
} else {
if (x >= 0) {
if constexpr (::tools::is_unsigned_v<::std::common_type_t<M, N>>) {
return 0;
} else {
return x / y;
}
} else {
return (x + 1) / y + 1;
}
}
}
}
#line 16 "tools/pow_mod_cache.hpp"
namespace tools {
template <class M>
class pow_mod_cache {
::std::vector<M> m_pow;
::std::vector<M> m_cumsum;
::std::vector<M> m_inv_pow;
::std::vector<M> m_inv_cumsum;
::std::optional<::std::pair<long long, long long>> m_period;
public:
pow_mod_cache() = default;
explicit pow_mod_cache(const M base) : m_pow({M(1), base}), m_cumsum({M::raw(0)}), m_inv_pow({M(1)}), m_inv_cumsum({M::raw(0)}) {
if (base == M(-1)) {
if (M::mod() > 2) {
this->m_period = ::std::make_pair(0LL, 2LL);
} else {
this->m_period = ::std::make_pair(0LL, 1LL);
this->m_pow.resize(1);
}
this->m_inv_pow.clear();
this->m_inv_cumsum.clear();
}
}
template <typename Z, ::std::enable_if_t<::std::is_integral_v<Z>, ::std::nullptr_t> = nullptr>
explicit pow_mod_cache(const Z base) : pow_mod_cache(M(base)) {
}
M operator[](const long long n) {
if (!this->m_period) {
if (::std::max<long long>(::std::ssize(this->m_pow) - 1, n) - ::std::min<long long>(n, -(::std::ssize(this->m_inv_pow) - 1)) + 1 < M::mod() - 1) {
if (n >= 0) {
const long long size = ::std::ssize(this->m_pow);
this->m_pow.resize(::std::max(size, n + 1));
for (long long i = size; i < ::std::ssize(this->m_pow); ++i) {
this->m_pow[i] = this->m_pow[i - 1] * this->m_pow[1];
}
return this->m_pow[n];
} else {
if (this->m_inv_pow.size() == 1) {
this->m_inv_pow.push_back(this->m_pow[1].inv());
}
const long long size = ::std::ssize(this->m_inv_pow);
this->m_inv_pow.resize(::std::max(size, -n + 1));
for (long long i = size; i < ::std::ssize(this->m_inv_pow); ++i) {
this->m_inv_pow[i] = this->m_inv_pow[i - 1] * this->m_inv_pow[1];
}
return this->m_inv_pow[-n];
}
}
this->m_period = ::tools::find_cycle(this->m_pow[0], [&](const M& prev) { return prev * this->m_pow[1]; });
const long long size = ::std::ssize(this->m_pow);
this->m_pow.resize(this->m_period->first + this->m_period->second);
for (long long i = size; i < ::std::ssize(this->m_pow); ++i) {
this->m_pow[i] = this->m_pow[i - 1] * this->m_pow[1];
}
this->m_inv_pow.clear();
this->m_inv_cumsum.clear();
}
if (this->m_period->first == 0) {
return this->m_pow[::tools::mod(n, this->m_period->second)];
} else {
assert(n >= 0);
if (n < this->m_period->first + this->m_period->second) {
return this->m_pow[n];
} else {
return this->m_pow[(n - this->m_period->first) % this->m_period->second + this->m_period->first];
}
}
}
M sum(const long long l, const long long r) {
if (l >= r) return M::raw(0);
(*this)[r - 1];
(*this)[l];
{
const long long size = ::std::ssize(this->m_cumsum);
this->m_cumsum.resize(this->m_pow.size() + 1);
for (long long i = size; i < ::std::ssize(this->m_cumsum); ++i) {
this->m_cumsum[i] = this->m_cumsum[i - 1] + this->m_pow[i - 1];
}
}
if (!this->m_period) {
const long long size = ::std::ssize(this->m_inv_cumsum);
this->m_inv_cumsum.resize(this->m_inv_pow.size() + 1);
for (long long i = size; i < ::std::ssize(this->m_inv_cumsum); ++i) {
this->m_inv_cumsum[i] = this->m_inv_cumsum[i - 1] + this->m_pow[i - 1];
}
if (l >= 0) {
return this->m_cumsum[r] - this->m_cumsum[l];
} else if (r <= 0) {
return this->m_inv_cumsum[-l] - this->m_inv_cumsum[-r];
} else {
return (this->m_inv_cumsum[-l] - this->m_inv_cumsum[1]) + (this->m_cumsum[r] - this->m_cumsum[0]);
}
}
static const auto cumsum = [&](const long long ll, const long long rr) {
return this->m_cumsum[rr] - this->m_cumsum[ll];
};
if (l >= 0) {
static const auto f = [&](const long long x) {
if (x <= this->m_period->first + this->m_period->second) {
return cumsum(0, x);
} else {
return cumsum(0, this->m_period->first) +
cumsum(this->m_period->first, this->m_period->first + this->m_period->second) * ((x - this->m_period->first) / this->m_period->second) +
cumsum(this->m_period->first, (x - this->m_period->first) % this->m_period->second + this->m_period->first);
}
};
return f(r) - f(l);
} else {
const auto& n = this->m_period->second;
return cumsum(::tools::mod(l, n), n) + cumsum(0, ::tools::mod(r, n)) + cumsum(0, n) * M(::tools::floor(r, n) - ::tools::ceil(l, n));
}
}
};
}
#line 1 "tools/now.hpp"
#include <chrono>
namespace tools {
inline long long now() {
return ::std::chrono::duration_cast<::std::chrono::nanoseconds>(::std::chrono::high_resolution_clock::now().time_since_epoch()).count();
}
}
#line 12 "tools/detail/rolling_hash.hpp"
namespace tools {
class rolling_hash;
class modint_for_rolling_hash {
private:
static constexpr ::std::uint64_t MASK30 = (::std::uint64_t(1) << 30) - 1;
static constexpr ::std::uint64_t MASK31 = (::std::uint64_t(1) << 31) - 1;
static constexpr ::std::uint64_t MOD = (::std::uint64_t(1) << 61) - 1;
static constexpr ::std::uint64_t MASK61 = MOD;
static constexpr ::std::uint64_t POSITIVIZER = MOD * 4;
::std::uint64_t m_val;
modint_for_rolling_hash(const ::std::uint64_t x, int) : m_val(x) {
}
static ::std::uint64_t mul(const ::std::uint64_t a, const ::std::uint64_t b) {
assert(a < MOD);
assert(b < MOD);
const ::std::uint64_t au = a >> 31;
const ::std::uint64_t ad = a & MASK31;
const ::std::uint64_t bu = b >> 31;
const ::std::uint64_t bd = b & MASK31;
const ::std::uint64_t mid = ad * bu + au * bd;
const ::std::uint64_t midu = mid >> 30;
const ::std::uint64_t midd = mid & MASK30;
return au * bu * 2 + midu + (midd << 31) + ad * bd;
}
static ::std::uint64_t calc_mod(const ::std::uint64_t x) {
const ::std::uint64_t xu = x >> 61;
const ::std::uint64_t xd = x & MASK61;
::std::uint64_t res = xu + xd;
if (res >= MOD) res -= MOD;
return res;
}
public:
modint_for_rolling_hash() = default;
modint_for_rolling_hash(const ::tools::modint_for_rolling_hash&) = default;
modint_for_rolling_hash(::tools::modint_for_rolling_hash&&) = default;
~modint_for_rolling_hash() = default;
::tools::modint_for_rolling_hash& operator=(const ::tools::modint_for_rolling_hash&) = default;
::tools::modint_for_rolling_hash& operator=(::tools::modint_for_rolling_hash&&) = default;
explicit modint_for_rolling_hash(const ::std::uint64_t x) : m_val(calc_mod(x)) {
}
::tools::modint_for_rolling_hash pow(const long long n) const {
return ::tools::pow(*this, n);
}
::tools::modint_for_rolling_hash inv() const {
assert(this->m_val != 0);
return ::tools::modint_for_rolling_hash(::std::get<0>(::tools::extgcd(this->m_val, MOD)));
}
::tools::modint_for_rolling_hash operator+() const {
return *this;
}
::tools::modint_for_rolling_hash operator-() const {
return ::tools::modint_for_rolling_hash(POSITIVIZER - this->m_val);
}
friend ::tools::modint_for_rolling_hash operator+(const ::tools::modint_for_rolling_hash& lhs, const ::tools::modint_for_rolling_hash& rhs) {
return ::tools::modint_for_rolling_hash(lhs.m_val + rhs.m_val);
}
::tools::modint_for_rolling_hash& operator+=(const ::tools::modint_for_rolling_hash& other) {
this->m_val = calc_mod(this->m_val + other.m_val);
return *this;
}
friend ::tools::modint_for_rolling_hash operator-(const ::tools::modint_for_rolling_hash& lhs, const ::tools::modint_for_rolling_hash& rhs) {
return ::tools::modint_for_rolling_hash(lhs.m_val + POSITIVIZER - rhs.m_val);
}
::tools::modint_for_rolling_hash& operator-=(const ::tools::modint_for_rolling_hash& other) {
this->m_val = calc_mod(this->m_val + POSITIVIZER - other.m_val);
return *this;
}
friend ::tools::modint_for_rolling_hash operator*(const ::tools::modint_for_rolling_hash& lhs, const ::tools::modint_for_rolling_hash& rhs) {
return ::tools::modint_for_rolling_hash(mul(lhs.m_val, rhs.m_val));
}
::tools::modint_for_rolling_hash& operator*=(const ::tools::modint_for_rolling_hash& other) {
this->m_val = calc_mod(mul(this->m_val, other.m_val));
return *this;
}
friend ::tools::modint_for_rolling_hash operator/(const ::tools::modint_for_rolling_hash& lhs, const ::tools::modint_for_rolling_hash& rhs) {
return ::tools::modint_for_rolling_hash(mul(lhs.m_val, rhs.inv().m_val));
}
::tools::modint_for_rolling_hash& operator/=(const ::tools::modint_for_rolling_hash& other) {
this->m_val = calc_mod(mul(this->m_val, other.inv().m_val));
return *this;
}
::tools::modint_for_rolling_hash& operator++() {
this->m_val = calc_mod(this->m_val + 1);
return *this;
}
::tools::modint_for_rolling_hash operator++(int) {
const auto result = *this;
++(*this);
return result;
}
::tools::modint_for_rolling_hash& operator--() {
this->m_val = calc_mod(this->m_val + POSITIVIZER - 1);
return *this;
}
::tools::modint_for_rolling_hash operator--(int) {
const auto result = *this;
--(*this);
return result;
}
friend bool operator==(const ::tools::modint_for_rolling_hash& lhs, const ::tools::modint_for_rolling_hash& rhs) {
return lhs.m_val == rhs.m_val;
}
friend bool operator!=(const ::tools::modint_for_rolling_hash& lhs, const ::tools::modint_for_rolling_hash& rhs) {
return lhs.m_val != rhs.m_val;
}
long long val() const {
return this->m_val;
}
static ::tools::modint_for_rolling_hash raw(const ::std::uint64_t x) {
return ::tools::modint_for_rolling_hash(x, 0);
}
static long long mod() {
return MOD;
}
friend ::tools::rolling_hash;
};
class rolling_hash {
private:
using mint = ::tools::modint_for_rolling_hash;
inline static ::tools::pow_mod_cache<mint> m_pow_base = ::tools::pow_mod_cache<mint>(::tools::now());
::std::vector<mint> m_hash;
public:
rolling_hash() = default;
rolling_hash(const ::tools::rolling_hash&) = default;
rolling_hash(::tools::rolling_hash&&) = default;
~rolling_hash() = default;
::tools::rolling_hash& operator=(const ::tools::rolling_hash&) = default;
::tools::rolling_hash& operator=(::tools::rolling_hash&&) = default;
template <typename InputIterator>
rolling_hash(InputIterator begin, InputIterator end) {
this->m_hash.push_back(mint::raw(0));
const auto base = m_pow_base[1].m_val;
for (auto it = begin; it != end; ++it) {
this->m_hash.emplace_back(mint::mul(this->m_hash.back().m_val, base) + *it);
}
m_pow_base[this->m_hash.size()];
}
mint pow_base(const ::std::size_t i) const {
return m_pow_base[i];
}
mint slice(const ::std::size_t l, const ::std::size_t r) const {
assert(l <= r && r <= this->m_hash.size());
return mint(this->m_hash[r].m_val + mint::POSITIVIZER - mint::mul(this->m_hash[l].m_val, m_pow_base[r - l].m_val));
}
};
}
#line 5 "tools/modint_for_rolling_hash.hpp"
#line 9 "tests/has_mod.test.cpp"
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
assert_that(!tools::has_mod_v<int>);
assert_that(!tools::has_mod_v<std::string>);
assert_that(tools::has_mod_v<atcoder::modint998244353>);
assert_that(tools::has_mod_v<atcoder::modint>);
assert_that(tools::has_mod_v<tools::modint_for_rolling_hash>);
assert_that(!tools::has_mod_v<std::vector<atcoder::modint998244353>>);
assert_that(!tools::has_mod_v<std::vector<atcoder::modint>>);
assert_that(!tools::has_mod_v<std::vector<tools::modint_for_rolling_hash>>);
return 0;
}