結果

問題 No.856 増える演算
ユーザー fumiphysfumiphys
提出日時 2019-08-10 16:39:59
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 177 ms / 3,153 ms
コード長 8,200 bytes
コンパイル時間 2,281 ms
コンパイル使用メモリ 185,428 KB
実行使用メモリ 40,236 KB
最終ジャッジ日時 2024-07-19 17:12:09
合計ジャッジ時間 15,735 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 129 ms
39,320 KB
testcase_01 AC 125 ms
39,320 KB
testcase_02 AC 127 ms
39,320 KB
testcase_03 AC 126 ms
39,316 KB
testcase_04 AC 127 ms
39,316 KB
testcase_05 AC 123 ms
39,320 KB
testcase_06 AC 127 ms
39,324 KB
testcase_07 AC 126 ms
39,320 KB
testcase_08 AC 126 ms
39,324 KB
testcase_09 AC 129 ms
39,448 KB
testcase_10 AC 127 ms
39,244 KB
testcase_11 AC 125 ms
39,192 KB
testcase_12 AC 129 ms
39,192 KB
testcase_13 AC 126 ms
39,196 KB
testcase_14 AC 125 ms
39,328 KB
testcase_15 AC 131 ms
39,324 KB
testcase_16 AC 131 ms
39,196 KB
testcase_17 AC 127 ms
39,324 KB
testcase_18 AC 127 ms
39,452 KB
testcase_19 AC 127 ms
39,320 KB
testcase_20 AC 124 ms
39,196 KB
testcase_21 AC 126 ms
39,324 KB
testcase_22 AC 124 ms
39,324 KB
testcase_23 AC 124 ms
39,508 KB
testcase_24 AC 127 ms
39,272 KB
testcase_25 AC 128 ms
39,468 KB
testcase_26 AC 120 ms
39,324 KB
testcase_27 AC 125 ms
39,196 KB
testcase_28 AC 129 ms
39,380 KB
testcase_29 AC 127 ms
39,492 KB
testcase_30 AC 126 ms
39,236 KB
testcase_31 AC 126 ms
39,344 KB
testcase_32 AC 127 ms
39,384 KB
testcase_33 AC 128 ms
39,432 KB
testcase_34 AC 130 ms
39,548 KB
testcase_35 AC 132 ms
39,588 KB
testcase_36 AC 130 ms
39,532 KB
testcase_37 AC 127 ms
39,500 KB
testcase_38 AC 128 ms
39,344 KB
testcase_39 AC 126 ms
39,232 KB
testcase_40 AC 123 ms
39,408 KB
testcase_41 AC 126 ms
39,412 KB
testcase_42 AC 131 ms
39,572 KB
testcase_43 AC 124 ms
39,412 KB
testcase_44 AC 128 ms
39,204 KB
testcase_45 AC 125 ms
39,356 KB
testcase_46 AC 130 ms
39,416 KB
testcase_47 AC 128 ms
39,288 KB
testcase_48 AC 126 ms
39,476 KB
testcase_49 AC 126 ms
39,360 KB
testcase_50 AC 127 ms
39,360 KB
testcase_51 AC 133 ms
39,412 KB
testcase_52 AC 130 ms
39,560 KB
testcase_53 AC 151 ms
39,728 KB
testcase_54 AC 139 ms
39,496 KB
testcase_55 AC 150 ms
39,588 KB
testcase_56 AC 138 ms
39,468 KB
testcase_57 AC 154 ms
39,764 KB
testcase_58 AC 147 ms
39,636 KB
testcase_59 AC 161 ms
39,948 KB
testcase_60 AC 142 ms
39,680 KB
testcase_61 AC 161 ms
39,968 KB
testcase_62 AC 159 ms
39,880 KB
testcase_63 AC 129 ms
39,340 KB
testcase_64 AC 160 ms
39,824 KB
testcase_65 AC 143 ms
39,432 KB
testcase_66 AC 143 ms
39,672 KB
testcase_67 AC 156 ms
39,660 KB
testcase_68 AC 162 ms
39,872 KB
testcase_69 AC 161 ms
39,844 KB
testcase_70 AC 170 ms
39,900 KB
testcase_71 AC 166 ms
40,020 KB
testcase_72 AC 160 ms
39,908 KB
testcase_73 AC 176 ms
39,980 KB
testcase_74 AC 173 ms
40,108 KB
testcase_75 AC 168 ms
40,232 KB
testcase_76 AC 177 ms
40,108 KB
testcase_77 AC 172 ms
40,112 KB
testcase_78 AC 168 ms
39,980 KB
testcase_79 AC 175 ms
40,112 KB
testcase_80 AC 165 ms
40,108 KB
testcase_81 AC 170 ms
40,236 KB
testcase_82 AC 153 ms
40,108 KB
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 # 

// includes
#include <bits/stdc++.h>

// macros
#define pb emplace_back
#define mk make_pair
#define pq priority_queue
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define vrep(v, i) for(int i = 0; i < (v).size(); i++)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define FI first
#define SE second
#define bit(n) (1LL<<(n))
#define INT(n) int n; cin >> n;
#define LL(n) ll n; cin >> n;
#define DOUBLE(n) double n; cin >> n;
using namespace std;

template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}
template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << p.first << " " << p.second; return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}

//  types
using ll = long long int;
using P = pair<int, int>;
using Pli = pair<ll, int>;
using Pil = pair<int, ll>;
using Pll = pair<ll, ll>;
using Pdd = pair<double, double>;
using cd = complex<double>;

// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1e9 + 7;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};

// solve

template <typename T>
T power(T a, T n, T mod) {
  n = n % (mod - 1);
  T res = 1;
  T tmp = n;
  T curr = a;
  while(tmp){
    if(tmp % 2 == 1){
      res = (T)(res * curr % mod);
    }
    curr = (T)(curr * curr % mod);
    tmp >>= 1;
  }

  return res;
}


template<typename T>
T extgcd(T a, T b, T &x, T &y){ 
  T d = a;
  if(b != 0){
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  }else{
    x = 1, y = 0;
  }
  return d;
}

template <typename T>
T modinv(T a, T m){
  long long x = 0, y = 0;
  extgcd<long long>(a, m, x, y);
  x %= m;
  if(x < 0)x += m;
  return x;
}
template <int MOD, int g>
struct NTT{
  int get_mod(){
    return MOD;
  }
  void _ntt(vector<long long> &f, bool inv=false){
    int n = f.size(), mask = n - 1;
    int h = power<long long>(g, (MOD - 1) / n, MOD);
    if(inv)h = modinv(h, MOD);
    vector<long long> tmp(n);
    for(int i = n >> 1; i >= 1; i >>= 1){
      long long zeta = power<long long>(h, i, MOD);
      long long w = 1;
      for(int j = 0; j < n; j += i){
        for(int k = 0; k < i; k++){
          tmp[j+k] = (f[((j<<1)&mask)+k] + w * f[(((j<<1)+i)&mask)+k] % MOD) % MOD;
        }
        w = w * zeta % MOD;
      }
      swap(f, tmp);
    }
  }
  void ntt(vector<long long> &f){
    _ntt(f, false);
  }
  void intt(vector<long long> &f){
    _ntt(f, true);
    int n = f.size();
    int ni = modinv(n, MOD);
    for(int i = 0; i < n; i++)f[i] = f[i] * ni % MOD;
  }
  vector<long long> convolution(vector<long long> f, vector<long long> h){
    int n = 1;
    while(n < int(f.size() + h.size()))n *= 2;
    f.resize(n, 0); h.resize(n, 0);
    ntt(f);
    ntt(h);
    for(int i = 0; i < n; i++)f[i] = f[i] * h[i] % MOD;
    intt(f);
    return f;
  }
};

using NTT1 = NTT<167772161, 3>;
using NTT2 = NTT<469762049, 3>;
using NTT3 = NTT<1224736769, 3>;

template <typename T>
long long garner(vector<T> b, vector<T> m, T MOD){
  m.emplace_back(MOD);
  vector<long long> coef(m.size(), 1);
  vector<long long> consts(m.size(), 0);
  for(int i = 0; i < b.size(); i++){
    long long t = ((b[i] - consts[i]) % m[i]) * modinv<long long>(coef[i], m[i]) % m[i];
    for(int j = i + 1; j < m.size(); j++){
      consts[j] = (consts[j] + t * coef[j] % m[j]) % m[j];
      coef[j] = coef[j] * m[i] % m[j];
    }
  }
  return consts.back();
}


vector<long long> arbitrary_mod_convolution(vector<long long> f, vector<long long> g, int MOD){
  for(size_t i = 0; i < f.size(); i++)f[i] %= MOD;
  for(size_t i = 0; i < g.size(); i++)g[i] %= MOD;
  NTT1 ntt1;
  NTT2 ntt2;
  NTT3 ntt3;
  auto x1 = ntt1.convolution(f, g);
  auto x2 = ntt2.convolution(f, g);
  auto x3 = ntt3.convolution(f, g);

  vector<long long> res(x1.size());
  vector<long long> b(3), m(3);
  m[0] = ntt1.get_mod();
  m[1] = ntt2.get_mod();
  m[2] = ntt3.get_mod();
  for(size_t i = 0; i < x1.size(); i++){
    b[0] = x1[i];
    b[1] = x2[i];
    b[2] = x3[i];
    res[i] = garner<long long>(b, m, MOD);
  }
  return res;
}


// f.size() should be the power of 2.
void fft(vector<cd> &f, bool inv=false){
  int n = f.size(), mask = n - 1;
  vector<cd> tmp(n);
  for(int i = n >> 1; i >= 1; i >>= 1){
    cd zeta = polar(1., 2. * M_PI * i * (inv ? -1.: 1.) / n);
    cd w = 1;
    for(int j = 0; j < n; j += i){
      for(int k = 0; k < i; k++){
        tmp[j + k] = f[((j<<1)&mask) + k] + w * f[(((j<<1)+i)&mask)+k];
      }
      w *= zeta;
    }
    swap(f, tmp);
  }
}

void dft(vector<cd> &f){
  fft(f);
}

void idft(vector<cd> &f){
  fft(f, true);
  for(size_t i = 0; i < f.size(); i++)f[i] = f[i] / cd(f.size());
}

template <typename T>
vector<T> convolution(vector<T> &f, vector<T> &g){
  int n = 1;
  while(n < 2 * f.size() + 1)n *= 2;
  vector<cd> F(n, 0), G(n, 0);
  for(int i = 0; i < f.size(); i++)F[i] = cd(f[i]);
  for(int i = 0; i < g.size(); i++)G[i] = cd(g[i]);

  dft(F);
  dft(G);
  vector<cd> H(n);
  for(int i = 0; i < n; i++)H[i] = F[i] * G[i];
  idft(H);
  vector<T> h(n);
  for(int i = 0; i < n; i++){
    h[i] = T(round(H[i].real()));
  }
  return h;
}


int main(int argc, char const* argv[])
{
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(20);
  INT(n); vector<ll> a(n); cin >> a;
  ll res = 1;
  ll sum = a[n-1];
  rrep(i, n - 1){
    res = res * power<ll>(a[i], sum, mod) % mod;
    sum += a[i];
  }

  vector<ll> b(2e5+1, 0);
  rep(i, n)b[a[i]]++;
  vector<ll> bt = b;
  //auto f = arbitrary_mod_convolution(b, b, mod);
  auto f = convolution(b, bt);
  /*NTT1 ntt1;
    auto f = ntt1.convolution(b, b);*/
  rep(i, n)f[a[i] * 2]--;
  rep(i, sz(f))f[i] /= 2;
  /*rep(i, 10)cout << b[i] << "\n "[i + 1 != 10];
  rep(i, 10)cout << b[i] << "\n "[i + 1 != 10];
  rep(i, 10)cout << f[i] << "\n "[i + 1 != 10];*/
  FOR(i, 1, sz(f)){
    res = res * power<ll>(i, f[i], mod) % mod;
  }

  ll am = a[n-1];
  double mini = 1e18;
  ll prod = 1;
  rrep(i, n - 1){
    double tmp = log(a[i] + am) + am * log(a[i]);
    if(tmp < mini){
      mini = tmp;
      prod = (am + a[i]) * power<ll>(a[i], am, mod) % mod;
    }
    am = min(am, a[i]);
  }
  res = res * modinv<ll>(prod, mod) % mod;

  cout << res << endl;
  return 0;
}
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