config1: compile command
-std=gnu++2a -D LOCAL -Wall -Wextra -O2 -Wshadow -Wformat=2 -Wfloat-equal -Wconversion -Wlogical-op -Wshift-overflow=2 -Wduplicated-cond -Wcast-qual -Wcast-align
-std=gnu++2a -D LOCAL
-H stdc++.h
-H dbg.h config2: fake bits/stdc++.h for faster compile
#include <algorithm>
#include <array>
#include <bit>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <ranges>
#include <set>
#include <span>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#include <valarray>
template with Modular
#pragma region github_funcdfs // clang-format off
#include <bits/stdc++.h>
/* using golang types */ using namespace std; using int32 = signed; using uint32 = unsigned; using float32 = double; using int64 = long long; using uint64 = unsigned long long; using float64 = long double;
/* vec<(any)> cincout */ template <class T> istream &operator>> (istream &cin, vector<T> &a) { for (auto &x : a) { cin >> x; } return cin; }
template <class T> ostream &operator<< (ostream &cout, vector<T> &a) { int n = int(a.size()); if (!n) { return cout; } cout << a[0]; for (int i = 1; i < n; i++) { cout << ' ' << a[i]; } return cout; }
template <class T> istream &operator>> (istream &cin, valarray<T> &a) { for (auto &x : a) { cin >> x; } return cin; }
template <class T> ostream &operator<< (ostream &cout, valarray<T> &a) { int n = int(a.size()); if (!n) { return cout; } cout << a[0]; for (int i = 1; i < n; i++) { cout << ' ' << a[i]; } return cout; }
template <class T> ostream &operator<< (ostream &cout, vector<vector<T>> &a) { int n = int(a.size()); if (!n) { return cout; } cout << a[0]; for (int i = 1; i < n; i++) { cout << '\n' << a[i]; } return cout; }
template <class T> ostream &operator<< (ostream &cout, vector<valarray<T>> &a) { int n = int(a.size()); if (!n) { return cout; } cout << a[0]; for (int i = 1; i < n; i++) { cout << '\n' << a[i]; } return cout; }
#define endl '\n' /* Use '\n' instead of std::endl to avoid unnecessary buffer flushes for performance */
#define print(...) std::cout << format(__VA_ARGS__) /* C++23 std::print() -> the format string is printed to the standard output */
#define println(...) std::cout << format("{0}\n", __VA_ARGS__); /* C++23 std::println() -> to print a single value and append a newline */
struct _init_end { _init_end() { std::cout << fixed << setprecision( 15 /* float output precision */); { cin.tie(nullptr); ios::sync_with_stdio(false); }}} __author_github_funcdfs;
#ifdef LOCAL /* For local debugging purposes */
#include "algo/dbg.h"
#else
#define dbg(...) ;
#define eprint(...) ;
#define eprintln(...) ;
#endif
#pragma endregion github_funcdfs // clang-format on
#pragma region Modular_DefineCode // clang-format off
template <typename T> T inverse(T a, T m) {
T u = 0, v = 1; while (a != 0) { T t = m / a;
m -= t * a; swap(a, m); u -= t * v; swap(u, v); }
assert(m == 1); return u; }
template <typename T> class Modular { public:
using Type = typename decay<decltype(T::value)>::type;
constexpr Modular() : value() {}
template <typename U> Modular(const U& x) { value = normalize(x); }
template <typename U> static Type normalize(const U& x) { Type v;
if (-mod() <= x && x < mod()) { v = static_cast<Type>(x); }
else {v = static_cast<Type>(x % mod());} if (v < 0) v += mod(); return v; }
const Type& operator()() const { return value; }
template <typename U> explicit operator U() const { return static_cast<U>(value); }
constexpr static Type mod() { return T::value; }
Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
Modular& operator++() { return *this += 1; }
Modular& operator--() { return *this -= 1; }
Modular operator++(int) { Modular result(*this); *this += 1; return result; }
Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
Modular operator-() const { return Modular(-value); }
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value)); return *this; }
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) {
long long q = static_cast<long long>(static_cast<long double>(value) * rhs.value / mod());
value = normalize(value * rhs.value - q * mod()); return *this; }
template <typename U = T>
typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
value = normalize(value * rhs.value); return *this; }
Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
friend const Type& abs(const Modular& x) { return x.value; }
template <typename U> friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename U> friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename V, typename U> friend V& operator>>(V& stream, Modular<U>& number);
private:
Type value;
};
template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }
template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }
template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template<typename T, typename U> Modular<T> power(const Modular<T>& a, const U& b) {
assert(b >= 0); Modular<T> x = a, res = 1; U p = b;
while (p > 0) { if (p & 1) res *= x; x *= x; p >>= 1; } return res; }
template <typename T> bool IsZero(const Modular<T>& number) {
return number() == 0; }
template <typename T> string to_string(const Modular<T>& number) {
return to_string(number()); }
// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T> U& operator<<(U& stream, const Modular<T>& number) {
return stream << number(); }
// U == std::istream? but done this way because of fastinput
template <typename U, typename T> U& operator>>(U& stream, Modular<T>& number) {
typename common_type<typename Modular<T>::Type, long long>::type x;
stream >> x; number.value = Modular<T>::normalize(x); return stream; }
// inverse(a, m); power(a, b); C(n, k); Fact(n);
#pragma endregion Modular_DefineCode // clang-format on
// using ModType = int; /* dynamic mod */
// struct VarMod { static ModType value; };
// ModType VarMod::value;
// ModType& md = VarMod::value;
// using Mint = Modular<VarMod>;
constexpr int md = 1000000007; // 1000000007 998244353 2147483647 4294967295 9223372036854775807
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
// vector<Mint> fact(1, 1);
// vector<Mint> inv_fact(1, 1);
// Mint C(int n, int k) {
// if (k < 0 || k > n) {
// return 0;
// }
// while ((int) fact.size() < n + 1) {
// fact.push_back(fact.back() * (int) fact.size());
// inv_fact.push_back(1 / fact.back());
// }
// return fact[n] * inv_fact[k] * inv_fact[n - k];
// }
// vector<Mint> fact(1, 1);
// Mint F(int n) {
// while (int(fact.size()) < n + 1) {
// fact.push_back(fact.back() * (int)fact.size());
// }
// return fact[n];
// }
// ----------------------------- /* Start of useful functions */ -----------------------------
// ----------------------------- /* End of useful functions */ -------------------------------
head template without any function
#pragma region github_funcdfs // clang-format off
#include <bits/stdc++.h>
/* using golang types */ using namespace std; using int32 = signed; using uint32 = unsigned; using float32 = double; using int64 = long long; using uint64 = unsigned long long; using float64 = long double;
/* vec<(any)> cincout */ template <class T> istream &operator>> (istream &cin, vector<T> &a) { for (auto &x : a) { cin >> x; } return cin; }
template <class T> ostream &operator<< (ostream &cout, vector<T> &a) { int n = int(a.size()); if (!n) { return cout; } cout << a[0]; for (int i = 1; i < n; i++) { cout << ' ' << a[i]; } return cout; }
template <class T> istream &operator>> (istream &cin, valarray<T> &a) { for (auto &x : a) { cin >> x; } return cin; }
template <class T> ostream &operator<< (ostream &cout, valarray<T> &a) { int n = int(a.size()); if (!n) { return cout; } cout << a[0]; for (int i = 1; i < n; i++) { cout << ' ' << a[i]; } return cout; }
template <class T> ostream &operator<< (ostream &cout, vector<vector<T>> &a) { int n = int(a.size()); if (!n) { return cout; } cout << a[0]; for (int i = 1; i < n; i++) { cout << '\n' << a[i]; } return cout; }
template <class T> ostream &operator<< (ostream &cout, vector<valarray<T>> &a) { int n = int(a.size()); if (!n) { return cout; } cout << a[0]; for (int i = 1; i < n; i++) { cout << '\n' << a[i]; } return cout; }
#define endl '\n' /* Use '\n' instead of std::endl to avoid unnecessary buffer flushes for performance */
#define print(...) std::cout << format(__VA_ARGS__) /* C++23 std::print() -> the format string is printed to the standard output */
#define println(...) std::cout << format("{0}\n", __VA_ARGS__); /* C++23 std::println() -> to print a single value and append a newline */
struct _init_end { _init_end() { std::cout << fixed << setprecision( 15 /* float output precision */); { cin.tie(nullptr); ios::sync_with_stdio(false); }}} __author_github_funcdfs;
#ifdef LOCAL /* For local debugging purposes */
#include "algo/dbg.h"
#else
#define dbg(...) ;
#define eprint(...) ;
#define eprintln(...) ;
#endif
auto solve() -> void; /* main --> */ int32 main() { solve(); return 0; }
#pragma endregion github_funcdfs // clang-format on
// ----------------------------- /* Start of useful functions */ -----------------------------
auto solve() -> void {
return;
}
// ----------------------------- /* End of useful functions */ -------------------------------