結果

問題 No.1181 Product Sum for All Subsets
ユーザー Haar
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
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 27
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#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;
}
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