結果

問題 No.1181 Product Sum for All Subsets
ユーザー rokahikou1
提出日時 2020-08-28 03:48:05
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 42 ms / 2,000 ms
コード長 3,813 bytes
コンパイル時間 1,679 ms
コンパイル使用メモリ 169,952 KB
実行使用メモリ 8,064 KB
最終ジャッジ日時 2024-11-09 00:59:15
合計ジャッジ時間 3,385 ms
ジャッジサーバーID
(参考情報)
judge5 / judge1
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>
using namespace std;
#define rep(i, n) for(int(i) = 0; (i) < (n); (i)++)
#define FOR(i, m, n) for(int(i) = (m); (i) < (n); (i)++)
#define All(v) (v).begin(), (v).end()
#define pb push_back
#define MP(a, b) make_pair((a), (b))
template <class T> vector<T> make_vec(size_t a, T val) {
return vector<T>(a, val);
}
template <class T, class... Ts> auto make_vec(size_t a, Ts... ts) {
return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using Graph = vector<vector<int>>;
template <typename T> struct edge {
int to;
T cost;
edge(int t, T c) : to(t), cost(c) {}
};
template <typename T> using WGraph = vector<vector<edge<T>>>;
const int INF = 1 << 30;
const ll LINF = 1LL << 60;
const int MOD = 1e9 + 7;
template <uint_fast64_t MOD> class ModInt {
using u64 = uint_fast64_t;
public:
u64 val;
ModInt(const u64 x = 0) : val((x + MOD) % MOD) {}
constexpr u64 &value() { return val; }
constexpr ModInt operator-() { return val ? MOD - val : 0; }
constexpr ModInt operator+(const ModInt &rhs) const {
return ModInt(*this) += rhs;
}
constexpr ModInt operator-(const ModInt &rhs) const {
return ModInt(*this) -= rhs;
}
constexpr ModInt operator*(const ModInt &rhs) const {
return ModInt(*this) *= rhs;
}
constexpr ModInt operator/(const ModInt &rhs) const {
return ModInt(*this) /= rhs;
}
constexpr ModInt &operator+=(const ModInt &rhs) {
val += rhs.val;
if(val >= MOD) {
val -= MOD;
}
return *this;
}
constexpr ModInt &operator-=(const ModInt &rhs) {
if(val < rhs.val) {
val += MOD;
}
val -= rhs.val;
return *this;
}
constexpr ModInt &operator*=(const ModInt &rhs) {
val = val * rhs.val % MOD;
return *this;
}
constexpr ModInt &operator/=(const ModInt &rhs) {
*this *= rhs.inv();
return *this;
}
constexpr bool operator==(const ModInt &rhs) {
return this->val == rhs.val;
}
constexpr bool operator!=(const ModInt &rhs) {
return this->val != rhs.val;
}
friend constexpr ostream &operator<<(ostream &os, const ModInt<MOD> &x) {
return os << x.val;
}
friend constexpr istream &operator>>(istream &is, ModInt<MOD> &x) {
return is >> x.val;
}
constexpr ModInt inv() const { return ModInt(*this).pow(MOD - 2); }
constexpr ModInt pow(ll e) const {
u64 x = 1, p = val;
while(e > 0) {
if(e % 2 == 0) {
p = (p * p) % MOD;
e /= 2;
} else {
x = (x * p) % MOD;
e--;
}
}
return ModInt(x);
}
};
using mint = ModInt<MOD>;
//nCk mod.p;1<=k<=n<=1e7,pfor ModInt
template <class T> struct BiCoefficient {
vector<T> fac, finv, inv;
BiCoefficient(const int MAX) : fac(MAX), finv(MAX), inv(MAX) {
fac[0] = fac[1] = 1;
finv[0] = finv[1] = 1;
inv[1] = 1;
for(int i = 2; i < MAX; i++) {
fac[i] = fac[i - 1] * i;
inv[i] = -inv[MOD % i] * (MOD / i);
finv[i] = finv[i - 1] * inv[i];
}
}
T comb(int n, int k) {
if(n < k)
return 0;
if(n < 0 || k < 0)
return 0;
return fac[n] * finv[k] * finv[n - k];
}
};
int main() {
ll N, K;
cin >> N >> K;
mint Ksum = mint(K) * mint(K + 1) / mint(2);
mint res = 0;
BiCoefficient<mint> bicoef(201000);
for(int i = 0; i < N; i++) {
res += bicoef.comb(N, i) * mint(K).pow(N - i) * Ksum.pow(i);
}
cout << res << endl;
}
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