結果

問題 No.856 増える演算
ユーザー LayCurse
提出日時 2019-08-21 05:43:22
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 71 ms / 3,153 ms
コード長 12,304 bytes
コンパイル時間 2,809 ms
コンパイル使用メモリ 221,660 KB
最終ジャッジ日時 2025-01-07 14:27:27
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 80
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

#pragma GCC optimize ("Ofast")
#include<bits/stdc++.h>
using namespace std;
#define MD 1000000007
#define PI 3.14159265358979323846
void *wmem;
template<class S, class T> inline S min_L(S a,T b){
  return a<=b?a:b;
}
template<class S, class T> inline S max_L(S a,T b){
  return a>=b?a:b;
}
template<class T> inline void walloc1d(T **arr, int x, void **mem = &wmem){
  static int skip[16]={0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1};
  (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] );
  (*arr)=(T*)(*mem);
  (*mem)=((*arr)+x);
}
struct mint{
  static unsigned R, RR, Rinv, W, md, mdninv;
  unsigned val;
  mint(){
  }
  mint(int a){
    val = mulR(a);
  }
  mint(unsigned a){
    val = mulR(a);
  }
  mint(long long a){
    val = mulR(a);
  }
  mint(unsigned long long a){
    val = mulR(a);
  }
  int get_inv(long long a, int md){
    long long e, s=md, t=a, u=1, v=0;
    while(s){
      e=t/s;
      t-=e*s;
      u-=e*v;
      swap(t,s);
      swap(u,v);
    }
    if(u<0){
      u+=md;
    }
    return u;
  }
  void setmod(unsigned m){
    int i;
    unsigned t;
    W = 32;
    md = m;
    R = (1ULL << W) % md;
    RR = (unsigned long long)R*R % md;
    switch(m){
      case 104857601:
      Rinv = 2560000;
      mdninv = 104857599;
      break;
      case 998244353:
      Rinv = 232013824;
      mdninv = 998244351;
      break;
      case 1000000007:
      Rinv = 518424770;
      mdninv = 2226617417U;
      break;
      case 1000000009:
      Rinv = 171601999;
      mdninv = 737024967;
      break;
      case 1004535809:
      Rinv = 234947584;
      mdninv = 1004535807;
      break;
      case 1007681537:
      Rinv = 236421376;
      mdninv = 1007681535;
      break;
      case 1012924417:
      Rinv = 238887936;
      mdninv = 1012924415;
      break;
      case 1045430273:
      Rinv = 254466304;
      mdninv = 1045430271;
      break;
      case 1051721729:
      Rinv = 257538304;
      mdninv = 1051721727;
      break;
      default:
      Rinv = get_inv(R, md);
      mdninv = 0;
      t = 0;
      for(i=0;i<((int)W);i++){
        if(t%2==0){
          t+=md;
          mdninv |= (1U<<i);
        }
        t /= 2;
      }
    }
  }
  unsigned mulR(unsigned a){
    return (unsigned long long)a*R%md;
  }
  unsigned mulR(int a){
    if(a < 0){
      a = a%md+md;
    }
    return mulR((unsigned)a);
  }
  unsigned mulR(unsigned long long a){
    return mulR((unsigned)(a%md));
  }
  unsigned mulR(long long a){
    a %= md;
    if(a < 0){
      a += md;
    }
    return mulR((unsigned)a);
  }
  unsigned reduce(unsigned T){
    unsigned m=T * mdninv, t=(unsigned)((T + (unsigned long long)m*md) >> W);
    if(t >= md){
      t -= md;
    }
    return t;
  }
  unsigned reduce(unsigned long long T){
    unsigned m=(unsigned)T * mdninv, t=(unsigned)((T + (unsigned long long)m*md) >> W);
    if(t >= md){
      t -= md;
    }
    return t;
  }
  unsigned get(){
    return reduce(val);
  }
  mint &operator+=(mint a){
    val += a.val;
    if(val >= md){
      val -= md;
    }
    return *this;
  }
  mint &operator-=(mint a){
    if(val < a.val){
      val = val + md - a.val;
    }
    else{
      val -= a.val;
    }
    return *this;
  }
  mint &operator*=(mint a){
    val = reduce((unsigned long long)val*a.val);
    return *this;
  }
  mint &operator/=(mint a){
    return *this *= a.inverse();
  }
  mint operator+(mint a){
    return mint(*this)+=a;
  }
  mint operator-(mint a){
    return mint(*this)-=a;
  }
  mint operator*(mint a){
    return mint(*this)*=a;
  }
  mint operator/(mint a){
    return mint(*this)/=a;
  }
  mint operator+(int a){
    return mint(*this)+=mint(a);
  }
  mint operator-(int a){
    return mint(*this)-=mint(a);
  }
  mint operator*(int a){
    return mint(*this)*=mint(a);
  }
  mint operator/(int a){
    return mint(*this)/=mint(a);
  }
  mint operator+(long long a){
    return mint(*this)+=mint(a);
  }
  mint operator-(long long a){
    return mint(*this)-=mint(a);
  }
  mint operator*(long long a){
    return mint(*this)*=mint(a);
  }
  mint operator/(long long a){
    return mint(*this)/=mint(a);
  }
  mint operator-(void){
    mint res;
    if(val){
      res.val=md-val;
    }
    else{
      res.val=0;
    }
    return res;
  }
  operator bool(void){
    return val!=0;
  }
  operator int(void){
    return get();
  }
  operator long long(void){
    return get();
  }
  mint inverse(){
    int a=val, b=md, t, u=1, v=0;
    mint res;
    while(b){
      t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    if(u < 0){
      u += md;
    }
    res.val = (unsigned long long)u*RR % md;
    return res;
  }
  mint pw(unsigned long long b){
    mint a(*this), res;
    res.val = R;
    while(b){
      if(b&1){
        res *= a;
      }
      b >>= 1;
      a *= a;
    }
    return res;
  }
  bool operator==(int a){
    return mulR(a)==val;
  }
  bool operator!=(int a){
    return mulR(a)!=val;
  }
}
;
mint operator+(int a, mint b){
  return mint(a)+=b;
}
mint operator-(int a, mint b){
  return mint(a)-=b;
}
mint operator*(int a, mint b){
  return mint(a)*=b;
}
mint operator/(int a, mint b){
  return mint(a)/=b;
}
mint operator+(long long a, mint b){
  return mint(a)+=b;
}
mint operator-(long long a, mint b){
  return mint(a)-=b;
}
mint operator*(long long a, mint b){
  return mint(a)*=b;
}
mint operator/(long long a, mint b){
  return mint(a)/=b;
}
inline void rd(int &x){
  int k, m=0;
  x=0;
  for(;;){
    k = getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
inline void wt_L(char a){
  putchar_unlocked(a);
}
inline void wt_L(int x){
  char f[10];
  int m=0, s=0;
  if(x<0){
    m=1;
    x=-x;
  }
  while(x){
    f[s++]=x%10;
    x/=10;
  }
  if(!s){
    f[s++]=0;
  }
  if(m){
    putchar_unlocked('-');
  }
  while(s--){
    putchar_unlocked(f[s]+'0');
  }
}
inline void wt_L(mint x){
  int i;
  i = (int)x;
  wt_L(i);
}
template<class T, class S> inline T pow_L(T a, S b){
  T res=1;
  res = 1;
  while(b){
    if(b&1){
      res *= a;
    }
    b >>= 1;
    a *= a;
  }
  return res;
}
struct fft_pnt{
  double x, y;
  fft_pnt(void){
  }
  fft_pnt(double a, double b){
    x = a;
    y = b;
  }
  void set(double a, double b){
    x = a;
    y = b;
  }
  fft_pnt& operator+=(fft_pnt a){
    x+=a.x;
    y+=a.y;
    return *this;
  }
  fft_pnt& operator-=(fft_pnt a){
    x-=a.x;
    y-=a.y;
    return *this;
  }
  fft_pnt& operator*=(fft_pnt a){
    fft_pnt p=*this;
    x = p.x*a.x-p.y*a.y;
    y = p.x*a.y+p.y*a.x;
    return *this;
  }
  fft_pnt operator+(fft_pnt a){
    return fft_pnt(*this) += a;
  }
  fft_pnt operator-(fft_pnt a){
    return fft_pnt(*this) -= a;
  }
  fft_pnt operator*(fft_pnt a){
    return fft_pnt(*this) *= a;
  }
}
;
void fft_L(int n, fft_pnt x[], void *mem){
  double theta=2*PI / n, tmp;
  fft_pnt a, aa, b, bb, c, cc, d, dd, w1, w2, w3, *y=(fft_pnt*)mem;
  int i, j, n1, n2, n3, step=1;
  while(n > 2){
    n1 = n / 4;
    n2 = n1 + n1;
    n3 = n1 + n2;
    for(i=0;i<(n1);i++){
      w1 = fft_pnt(cos(i*theta),-sin(i*theta));
      w2 = w1*w1;
      w3 = w1*w2;
      for(j=0;j<(step);j++){
        a = x[j+step*i];
        b = x[j+step*(i+n1)];
        c = x[j+step*(i+n2)];
        d = x[j+step*(i+n3)];
        aa = a + c;
        bb = a - c;
        cc = b + d;
        dd = b - d;
        tmp = dd.y;
        dd.y = dd.x;
        dd.x = -tmp;
        y[j+step*(4*i  )] = aa + cc;
        y[j+step*(4*i+1)] = w1*(bb - dd);
        y[j+step*(4*i+2)] = w2*(aa - cc);
        y[j+step*(4*i+3)] = w3*(bb + dd);
      }
    }
    n /= 4;
    step *= 4;
    theta *= 4;
    swap(x,y);
  }
  if(n==2){
    for(i=0;i<(step);i++){
      y[i] = x[i] + x[i+step];
      y[i+step] = x[i] - x[i+step];
    }
    n /= 2;
    step *= 2;
    theta *= 2;
    swap(x,y);
  }
  for(i=0;i<(step);i++){
    y[i] = x[i];
  }
}
void fftinv_L(int n, fft_pnt x[], void *mem){
  double theta=2*PI / n, tmp;
  fft_pnt a, aa, b, bb, c, cc, d, dd, w1, w2, w3, *y=(fft_pnt*)mem;
  int i, j, n1, n2, n3, step=1;
  while(n > 2){
    n1 = n / 4;
    n2 = n1 + n1;
    n3 = n1 + n2;
    for(i=0;i<(n1);i++){
      w1 = fft_pnt(cos(i*theta),sin(i*theta));
      w2 = w1*w1;
      w3 = w1*w2;
      for(j=0;j<(step);j++){
        a = x[j+step*i];
        b = x[j+step*(i+n1)];
        c = x[j+step*(i+n2)];
        d = x[j+step*(i+n3)];
        aa = a + c;
        bb = a - c;
        cc = b + d;
        dd = b - d;
        tmp = dd.y;
        dd.y = dd.x;
        dd.x = -tmp;
        y[j+step*(4*i  )] = aa + cc;
        y[j+step*(4*i+1)] = w1*(bb + dd);
        y[j+step*(4*i+2)] = w2*(aa - cc);
        y[j+step*(4*i+3)] = w3*(bb - dd);
      }
    }
    n /= 4;
    step *= 4;
    theta *= 4;
    swap(x,y);
  }
  if(n==2){
    for(i=0;i<(step);i++){
      y[i] = x[i] + x[i+step];
      y[i+step] = x[i] - x[i+step];
    }
    n /= 2;
    step *= 2;
    theta *= 2;
    swap(x,y);
  }
  for(i=0;i<(step);i++){
    y[i] = x[i];
  }
}
void convolution_L(double A[], int As, double B[], int Bs, double res[], int Rs, void *mem = wmem){
  double mul;
  fft_pnt *a, *b;
  int i, n, n2;
  n =max_L(As+Bs, Rs);
  for(n2=1;n2<n;n2*=2){
    ;
  }
  walloc1d(&a, n2, &mem);
  walloc1d(&b, n2, &mem);
  for(i=0;i<(As);i++){
    a[i].set(A[i], 0);
  }
  for(i=(As);i<(n2);i++){
    a[i].set(0,0);
  }
  for(i=0;i<(Bs);i++){
    b[i].set(B[i], 0);
  }
  for(i=(Bs);i<(n2);i++){
    b[i].set(0,0);
  }
  fft_L(n2, a, mem);
  fft_L(n2, b, mem);
  for(i=0;i<(n2);i++){
    a[i] *= b[i];
  }
  fftinv_L(n2, a, mem);
  mul = 1.0 / n2;
  for(i=0;i<(Rs);i++){
    res[i] = a[i].x * mul;
  }
}
void convolution_L(double A[], int As, double res[], int Rs, void *mem = wmem){
  double mul;
  fft_pnt *a;
  int i, n, n2;
  n =max_L(As+As, Rs);
  for(n2=1;n2<n;n2*=2){
    ;
  }
  walloc1d(&a, n2, &mem);
  for(i=0;i<(As);i++){
    a[i].set(A[i], 0);
  }
  for(i=(As);i<(n2);i++){
    a[i].set(0,0);
  }
  fft_L(n2, a, mem);
  for(i=0;i<(n2);i++){
    a[i] *= a[i];
  }
  fftinv_L(n2, a, mem);
  mul = 1.0 / n2;
  for(i=0;i<(Rs);i++){
    res[i] = a[i].x * mul;
  }
}
char memarr[96000000];
unsigned mint::R, mint::RR, mint::Rinv, mint::W, mint::md, mint::mdninv;
int N;
int A[100000];
double c[100001];
double cnv[200001];
long long s[100001];
int mn[100001];
int main(){
  double dmin, dtmp;
  int i;
  long long tk;
  mint res, tmp;
  wmem = memarr;
  {
    mint x;
    x.setmod(MD);
  }
  rd(N);
  {
    int Lj4PdHRW;
    for(Lj4PdHRW=0;Lj4PdHRW<(N);Lj4PdHRW++){
      rd(A[Lj4PdHRW]);
    }
  }
  res = 1;
  for(i=0;i<(N);i++){
    c[A[i]]++;
  }
  convolution_L(c, 100001, cnv, 200001);
  for(i=0;i<(N);i++){
    cnv[2*A[i]]--;
  }
  for(i=0;i<(200001);i++){
    tk = (long long)(cnv[i]/2 + 0.5);
    if(tk){
      res *= (pow_L(mint(i),tk));
    }
  }
  for(i=N-1;i>=0;i--){
    s[i] = s[i+1] + A[i];
  }
  for(i=0;i<(N);i++){
    res *= (pow_L(mint(A[i]),s[i+1]));
  }
  mn[N] = 1073709056;
  for(i=N-1;i>=0;i--){
    mn[i] =min_L(mn[i+1], A[i]);
  }
  dmin = 1e300;
  for(i=N-2;i>=0;i--){
    dtmp = log(A[i] + mn[i+1]) + log(A[i]) * mn[i+1];
    if(dtmp < dmin){
      dmin = dtmp;
      tmp = (A[i] + mn[i+1]) * (pow_L(mint(A[i]),mn[i+1]));
    }
  }
  res /= tmp;
  wt_L(res);
  wt_L('\n');
  return 0;
}
// cLay varsion 20190820-1
// --- original code ---
// int N, A[1d5];
// 
// double c[100001], cnv[200001];
// ll s[100001];
// int mn[100001];
// {
//   int i;
//   ll tk;
//   mint res, tmp;
//   double dmin, dtmp;
// 
//   rd(N,A(N));
// 
//   res = 1;
//   
//   rep(i,N) c[A[i]]++;
//   convolution(c, 100001, cnv, 200001);
//   rep(i,N) cnv[2A[i]]--;
// 
//   rep(i,200001){
//     tk = (ll)(cnv[i]/2 + 0.5);
//     if(tk) res *= (mint(i) ** tk);
//   }
// 
//   for(i=N-1;i>=0;i--) s[i] = s[i+1] + A[i];
//   rep(i,N) res *= (mint(A[i]) ** s[i+1]);
// 
//   mn[N] = int_inf;
//   for(i=N-1;i>=0;i--) mn[i] = min(mn[i+1], A[i]);
// 
//   dmin = 1e300;
//   for(i=N-2;i>=0;i--){
//     dtmp = log(A[i] + mn[i+1]) + log(A[i]) * mn[i+1];
//     if(dtmp < dmin){
//       dmin = dtmp;
//       tmp = (A[i] + mn[i+1]) * ( mint(A[i]) ** mn[i+1] );
//     }
//   }
// 
//   res /= tmp;
//   wt(res);
// }
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0