結果
問題 | No.1181 Product Sum for All Subsets |
ユーザー |
|
提出日時 | 2020-08-21 22:09:10 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 42 ms / 2,000 ms |
コード長 | 4,569 bytes |
コンパイル時間 | 2,411 ms |
コンパイル使用メモリ | 198,496 KB |
最終ジャッジ日時 | 2025-01-13 05:56:31 |
ジャッジサーバーID (参考情報) |
judge3 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 27 |
ソースコード
#include <bits/stdc++.h>/*** @title Modint* @docs mint.md*/template <int32_t M> class ModInt{public:constexpr static int32_t MOD = M;uint32_t val;constexpr ModInt(): val(0){}constexpr ModInt(int64_t n){if(n >= M) val = n % M;else if(n < 0) val = n % M + M;else val = n;}constexpr auto& operator=(const ModInt &a){val = a.val; return *this;}constexpr auto& operator+=(const ModInt &a){if(val + a.val >= M) val = (uint64_t)val + a.val - M;else val += a.val;return *this;}constexpr auto& operator-=(const ModInt &a){if(val < a.val) val += M;val -= a.val;return *this;}constexpr auto& operator*=(const ModInt &a){val = (uint64_t)val * a.val % M;return *this;}constexpr auto& operator/=(const ModInt &a){val = (uint64_t)val * a.inv().val % M;return *this;}constexpr auto operator+(const ModInt &a) const {return ModInt(*this) += a;}constexpr auto operator-(const ModInt &a) const {return ModInt(*this) -= a;}constexpr auto operator*(const ModInt &a) const {return ModInt(*this) *= a;}constexpr auto operator/(const ModInt &a) const {return ModInt(*this) /= a;}constexpr bool operator==(const ModInt &a) const {return val == a.val;}constexpr bool operator!=(const ModInt &a) const {return val != a.val;}constexpr auto& operator++(){*this += 1; return *this;}constexpr auto& operator--(){*this -= 1; return *this;}constexpr auto operator++(int){auto t = *this; *this += 1; return t;}constexpr auto operator--(int){auto t = *this; *this -= 1; return t;}constexpr static ModInt power(int64_t n, int64_t p){if(p < 0) return power(n, -p).inv();int64_t ret = 1, e = n % M;for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M;return ret;}constexpr static ModInt inv(int64_t a){int64_t b = M, u = 1, v = 0;while(b){int64_t t = a / b;a -= t * b; std::swap(a,b);u -= t * v; std::swap(u,v);}u %= M;if(u < 0) u += M;return u;}constexpr static auto frac(int64_t a, int64_t b){return ModInt(a) / ModInt(b);}constexpr auto power(int64_t p) const {return power(val, p);}constexpr auto inv() const {return inv(val);}friend constexpr auto operator-(const ModInt &a){return ModInt(M-a.val);}friend constexpr auto operator+(int64_t a, const ModInt &b){return ModInt(a) + b;}friend constexpr auto operator-(int64_t a, const ModInt &b){return ModInt(a) - b;}friend constexpr auto operator*(int64_t a, const ModInt &b){return ModInt(a) * b;}friend constexpr auto operator/(int64_t a, const ModInt &b){return ModInt(a) / b;}friend std::istream& operator>>(std::istream &s, ModInt<M> &a){s >> a.val; return s;}friend std::ostream& operator<<(std::ostream &s, const ModInt<M> &a){s << a.val; return s;}template <int N>static auto div(){static auto value = inv(N);return value;}explicit operator int32_t() const noexcept {return val;}explicit operator int64_t() const noexcept {return val;}};/*** @title Factorial table* @docs factorial_table.md*/template <typename T> class FactorialTable{using value_type = T;std::vector<T> f_table;std::vector<T> if_table;public:FactorialTable(int N){f_table.assign(N+1, 1);if_table.assign(N+1, 1);for(int i = 1; i <= N; ++i){f_table[i] = f_table[i-1] * i;}if_table[N] = f_table[N].inv();for(int i = N-1; i >= 0; --i){if_table[i] = if_table[i+1] * (i+1);}}T factorial(int64_t i) const {assert(i < (int)f_table.size());return f_table[i];}T inv_factorial(int64_t i) const {assert(i < (int)if_table.size());return if_table[i];}T P(int64_t n, int64_t k) const {if(n < k or n < 0 or k < 0) return 0;return factorial(n) * inv_factorial(n-k);}T C(int64_t n, int64_t k) const {if(n < k or n < 0 or k < 0) return 0;return P(n,k) * inv_factorial(k);}T H(int64_t n, int64_t k) const {if(n == 0 and k == 0) return 1;return C(n+k-1, k);}};namespace solver{using mint = ModInt<1000000007>;void solve(){int64_t N, K; std::cin >> N >> K;auto ft = FactorialTable<mint>(N);mint ans = 0;mint s = mint(K) * mint(K + 1) / mint(2);for(int i = 0; i < N; ++i){ans += ft.C(N, i) * mint::power(K, N - i) * s.power(i);}std::cout << ans << "\n";}}int main(){solver::solve();return 0;}