結果

問題 No.856 増える演算
ユーザー SumitacchanSumitacchan
提出日時 2019-07-26 23:17:28
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
RE  
実行時間 -
コード長 6,237 bytes
コンパイル時間 1,785 ms
コンパイル使用メモリ 177,556 KB
実行使用メモリ 10,688 KB
最終ジャッジ日時 2024-07-02 09:34:26
合計ジャッジ時間 17,338 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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テストケース

テストケース表示
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ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(),v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL<<(n))
#define bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v) cout << #v << "=" << endl; REP(i_debug, v.size()){ cout << v[i_debug] << ","; } cout << endl;
#define mdebug(m) cout << #m << "=" << endl; REP(i_debug, m.size()){ REP(j_debug, m[i_debug].size()){ cout << m[i_debug][j_debug] << ","; } cout << endl;}
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for (auto &x : v) is >> x; return is; }
template<typename T> ostream &operator<<(ostream &os, vector<T> &v){ for(int i = 0; i < v.size(); i++) { cout << v[i]; if(i != v.size() - 1) cout << endl; }; return os; }
template<typename T> void Out(T x) { cout << x << endl; }
template<typename T1, typename T2> void Ans(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); }

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

//int dx[4] = {1,0,-1,0};
//int dy[4] = {0,1,0,-1};
//char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
//const int mod = 998244353;
#define Add(x, y) x = (x + (y)) % mod
#define Mult(x, y) x = (x * (y)) % mod

template<long long MOD>
struct ModInt{

    using ll = long long;
    ll val;

    void setval(ll v) { val = v % MOD; };
    ModInt(): val(0) {}
    ModInt(ll v) { setval(v); };

    ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); }
    ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); }
    ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); }
    ModInt operator/(const ModInt &x) const { return *this * x.inv(); }
    ModInt operator-() const { return ModInt(MOD - val); }
    ModInt operator+=(const ModInt &x) { return *this = *this + x; }
    ModInt operator-=(const ModInt &x) { return *this = *this - x; }
    ModInt operator*=(const ModInt &x) { return *this = *this * x; }
    ModInt operator/=(const ModInt &x) { return *this = *this / x; }

    friend ostream& operator<<(ostream &os, const ModInt &x) { os << x.val; return os; }
    friend istream& operator>>(istream &is, ModInt &x) { is >> x.val; x.val = (x.val % MOD + MOD) % MOD; return is; }

    ModInt pow(ll n) const {
        ModInt a = 1;
        if(n == 0) return a;
        int i0 = 64 - __builtin_clzll(n);
        for(int i = i0 - 1; i >= 0; i--){
            a = a * a;
            if((n >> i) & 1) a *= (*this); 
        }
        return a;
    }
    ModInt inv() const { return this->pow(MOD - 2); }
};

using mint = ModInt<mod>; mint pow(mint x, long long n) { return x.pow(n); }
//using mint = double; //for debug
using mvec = vector<mint>;
using mmat = vector<mvec>;

struct Combination{

    vector<mint> fact, invfact;

    Combination(int N){
        fact = vector<mint>({mint(1)});
        invfact = vector<mint>({mint(1)});
        fact_initialize(N);
    }

    void fact_initialize(int N){
        int i0 = fact.size();
        if(i0 >= N + 1) return;
        fact.resize(N + 1);
        invfact.resize(N + 1);
        for(int i = i0; i <= N; i++) fact[i] = fact[i - 1] * i;
        invfact[N] = (mint)1 / fact[N];
        for(int i = N - 1; i >= i0; i--) invfact[i] = invfact[i + 1] * (i + 1); 
    }

    mint nCr(int n, int r){
        if(n < 0 || r < 0 || r > n) return mint(0);
        if(fact.size() < n + 1) fact_initialize(n);
        return fact[n] * invfact[r] * invfact[n - r];
    }

    mint nPr(int n, int r){
        if(n < 0 || r < 0 || r > n) return mint(0);
        if(fact.size() < n + 1) fact_initialize(n);
        return fact[n] * invfact[n - r];
    }

};

//N=2^n, e^N=1
void FFT(vector<complex<long double>> &f, complex<long double> e){
    int N = f.size();
    if(N == 1) return;
    N /= 2;
    vector<complex<long double>> f0(N), f1(N);
    REP(i, N){
        f0[i] = f[2 * i];
        f1[i] = f[2 * i + 1];
    }
    complex<long double> e2 = e * e;
    FFT(f0, e2);
    FFT(f1, e2);

    complex<long double> c(1.0, 0.0);
    REP(i, N){
        f[i] = f0[i] + f1[i] * c;
        c *= e;
    }
    REP(i, N){
        f[i + N] = f0[i] + f1[i] * c;
        c *= e;
    }
}

vec conv(vec A, vec B){
    int n = bit(15);
    complex<long double> e(cos(2.0 * M_PI / n), sin(2.0 * M_PI / n));
    vector<complex<long double>> a(n, 0), b(n, 0);
    REP(i, SZ(A)){
        a[i] = complex<long double>(A[i], 0.0);
        b[i] = complex<long double>(B[i], 0.0);
    }
    FFT(a, e);
    FFT(b, e);
    REP(i, n) a[i] *= b[i];
    FFT(a, conj(e));
    vec C(n);
    REP(i, n) C[i] = (int)(a[i].real() / n + 0.5);
    return C;
}

signed main(){

    int N; cin >> N;
    vec A(N); cin >> A;
    
    long double vmin = INF;
    int m = A[0];
    mint mmin;
    FOR(i, 1, N){
        long double v = logl((long double)(m + A[i])) + (long double)A[i] * logl((long double)m);
        if(v < vmin){
            vmin = v;
            mmin = (mint)(m + A[i]) * pow((mint)m, A[i]);
        }
        Min(m, A[i]);
    }
    //debug(mmin);

    vec cnt(100001, 0);
    REP(i, N) cnt[A[i]]++;
    cnt = conv(cnt, cnt);
    REP(i, N) cnt[2 * A[i]]--;
    mint a1 = 1;
    REP(i, SZ(cnt)) a1 *= pow((mint)i, cnt[i] / 2);
    //debug(a1);

    mint a2 = 1;
    int s = 0;
    IREP(i, N){
        a2 *= pow((mint)A[i], s);
        s += A[i];
    }

    mint ans = a1 * a2 / mmin;
    Out(ans);

    return 0;
}
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