結果
| 問題 | No.1181 Product Sum for All Subsets |
| ユーザー |
 micheeeeell1001
|
| 提出日時 | 2020-08-21 23:12:57 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 51 ms / 2,000 ms |
| コード長 | 6,627 bytes |
| コンパイル時間 | 2,392 ms |
| コンパイル使用メモリ | 198,276 KB |
| 最終ジャッジ日時 | 2025-01-13 06:34:31 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge3 |
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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
#ifdef LOCAL
#define _GLIBCXX_DEBUG
#endif
#include<bits/stdc++.h>
using namespace std;
#define rep(i,s,t) for(ll i = (ll)(s); i < (ll)(t); i++)
#define rrep(i,s,t) for(ll i = (ll)(s-1);(ll)(t) <= i; i--)
#define all(x) (x).begin(), (x).end()
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> Pll;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
constexpr ll INF = numeric_limits<ll>::max()/4;
constexpr ll n_max = 2e5+10;
#define int ll
template <typename A, typename B>
string to_string(pair<A, B> p);
string to_string(const string &s) {return '"' + s + '"';}
string to_string(const char *c) {return to_string((string) c);}
string to_string(bool b) {return (b ? "true" : "false");}
template <size_t N>
string to_string(bitset<N> v){
string res = "";
for(size_t i = 0; i < N; i++) res += static_cast<char>('0' + v[i]);
return res;
}
template <typename A>
string to_string(A v) {
bool first = true;
string res = "{";
for(const auto &x : v) {
if(!first) res += ", ";
first = false;
res += to_string(x);
}
res += "}";
return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p){return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";}
void debug_out() {cerr << endl;}
template<typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
cerr << " " << to_string(H);
debug_out(T...);
}
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
template<class T>
bool chmax(T &a, T b){if(a < b){a = b; return true;} return false;}
template<class T>
bool chmin(T &a, T b){if(a > b){a = b; return true;} return false;}
template<std::int_fast64_t Modulus>
class modint {
using i64 = int_fast64_t;
public:
i64 a;
constexpr modint(const i64 x = 0) noexcept {
this -> a = x % Modulus;
if(a < 0){
a += Modulus;
}
}
constexpr int getmod() { return Modulus; }
constexpr modint operator - () const noexcept {
return a ? Modulus - a : 0;
}
constexpr const i64 &value() const noexcept {return a;}
constexpr modint operator+(const modint rhs) const noexcept {
return modint(*this) += rhs;
}
constexpr modint operator-(const modint rhs) const noexcept {
return modint(*this) -= rhs;
}
constexpr modint operator*(const modint rhs) const noexcept {
return modint(*this) *= rhs;
}
constexpr modint operator/(const modint rhs) const noexcept {
return modint(*this) /= rhs;
}
constexpr modint &operator+=(const modint rhs) noexcept {
a += rhs.a;
if(a >= Modulus) {
a -= Modulus;
}
return *this;
}
constexpr modint &operator-=(const modint rhs) noexcept {
if(a < rhs.a) {
a += Modulus;
}
a -= rhs.a;
return *this;
}
constexpr modint &operator*=(const modint rhs) noexcept {
a = a * rhs.a % Modulus;
return *this;
}
constexpr modint &operator/=(modint rhs) noexcept {
i64 a_ = rhs.a, b = Modulus, u = 1, v = 0;
while(b){
i64 t = a_/b;
a_ -= t * b; swap(a_,b);
u -= t * v; swap(u,v);
}
a = a * u % Modulus;
if(a < 0) a += Modulus;
return *this;
}
// 自前実装
constexpr bool operator==(const modint rhs) noexcept {
return a == rhs.a;
}
constexpr bool operator!=(const modint rhs) noexcept {
return a != rhs.a;
}
constexpr bool operator>(const modint rhs) noexcept {
return a > rhs.a;
}
constexpr bool operator>=(const modint rhs) noexcept {
return a >= rhs.a;
}
constexpr bool operator<(const modint rhs) noexcept {
return a < rhs.a;
}
constexpr bool operator<=(const modint rhs) noexcept {
return a <= rhs.a;
}
constexpr modint& operator++() noexcept {
return (*this) += modint(1);
}
// constexpr modint operator++(int) {
// modint tmp(*this);
// operator++();
// return tmp;
// }
constexpr modint& operator--() noexcept {
return (*this) -= modint(1);
}
// constexpr modint operator--(int) {
// modint tmp(*this);
// operator--();
// return tmp;
// }
template<typename T>
friend constexpr modint modpow(const modint &mt, T n) noexcept {
if(n < 0){
modint t = (modint(1) / mt);
return modpow(t, -n);
}
modint res = 1, tmp = mt;
while(n){
if(n & 1)res *= tmp;
tmp *= tmp;
n /= 2;
}
return res;
}
friend constexpr string to_string(const modint &mt) noexcept {
return to_string(mt.a);
}
};
// 標準入出力対応
template<std::int_fast64_t Modulus>
std::ostream &operator<<(std::ostream &out, const modint<Modulus> &m) {
out << m.a;
return out;
}
template<std::int_fast64_t Modulus>
std::istream &operator>>(std::istream &in, modint<Modulus> &m) {
ll a;
in >> a;
m = modint<Modulus>(a);
return in;
}
const ll MOD = 1e9+7;
// const ll MOD = 998244353;
using mint = modint<MOD>;
template<class T> struct BiCoef {
vector<T> fact_, inv_, finv_;
constexpr BiCoef() {}
constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
init(n);
}
constexpr void init(int n) noexcept {
fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
int MOD = fact_[0].getmod();
for(int i = 2; i < n; i++){
fact_[i] = fact_[i-1] * i;
inv_[i] = -inv_[MOD%i] * (MOD/i);
finv_[i] = finv_[i-1] * inv_[i];
}
}
constexpr T com(int n, int k) const noexcept {
if (n < k || n < 0 || k < 0) return 0;
return fact_[n] * finv_[k] * finv_[n-k];
}
constexpr T fact(int n) const noexcept {
if (n < 0) return 0;
return fact_[n];
}
constexpr T inv(int n) const noexcept {
if (n < 0) return 0;
return inv_[n];
}
constexpr T finv(int n) const noexcept {
if (n < 0) return 0;
return finv_[n];
}
};
BiCoef<mint> bc(n_max);
signed main(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
ll n; cin >> n;
ll k; cin >> k;
mint ans = 0;
mint sum = (mint(1) + mint(k)) * mint(k) / mint(2);
rep(i,0,n){
ans += bc.com(n, i) * modpow(sum, i) * modpow(mint(k), n - i);
}
cout << ans << "\n";
}