Submission #2090589

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Source Code Expand

#include<bits/stdc++.h>
using namespace std;
#define MD 1000000007
void *wmem;
template<class T> void walloc1d(T **arr, int x, void **mem = &wmem){
  (*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, u = 1, v = 0, t;
    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;}
};
unsigned mint::md, mint::W, mint::R, mint::Rinv, mint::mdninv, mint::RR;
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;
}
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;
  }
}
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');
  }
}
void wt_L(mint x){
  int i;
  i = (int)x;
  wt_L(i);
}
struct combination_mint{
  mint *fac, *ifac;
  void init(int n, void **mem = &wmem){
    int i;
    walloc1d(&fac, n, mem);
    walloc1d(&ifac, n, mem);
    fac[0] = 1;
    for(i=1;i<n;i++){
      fac[i] = fac[i-1] * i;
    }
    ifac[n-1] = 1 / fac[n-1];
    for(i=n-2;i>=0;i--){
      ifac[i] = ifac[i+1] * (i+1);
    }
  }
  mint C(int a, int b){
    if(b < 0 || b > a){
      return 0;
    }
    return fac[a]*ifac[b]*ifac[a-b];
  }
  mint P(int a, int b){
    if(b < 0 || b > a){
      return 0;
    }
    return fac[a]*ifac[a-b];
  }
  mint H(int a, int b){
    if(a==0 && b==0){
      return 1;
    }
    if(a<=0 || b<0){
      return 0;
    }
    return C(a+b-1, b);
  }
}
;
char memarr[96000000];
combination_mint comb;
int A[1100][1100], C[2200], K, N, X, Y, cur[2200], ok[2200], sz[2200][2], use[2200];
inline int nrm(int x){
  if(x < (x^X)){
    return x;
  }
  return x^X;
}
mint solve(int dep){
  int i, j, k, x;
  mint res, tmp;
  res = 0;
  if(dep==K){
    res = 1;
    for(i=0;i<2048;i++){
      use[i] = 0;
    }
    for(i=0;i<dep;i++){
      use[cur[i]]++;
    }
    for(i=0;i<2048;i++){
      if(use[i]){
        tmp = 0;
        for(j=0;j<use[i]+1;j++){
          if(j <= sz[i][0] && use[i]-j <= sz[i][1]){
            tmp += comb.C(use[i], j);
          }
        }
        res *= tmp;
      }
    }
    return res;
  }
  if(dep==0){
    for(i=0;i<2048;i++){
      if(ok[i]){
        ok[i]--;
        cur[dep] = i;
        res += solve(dep+1);
        ok[i]++;
      }
    }
    return res;
  }
  x = nrm(A[0][dep] ^ cur[0]);
  if(ok[x]){
    for(i=0;i<dep;i++){
      if(x != nrm(A[i][dep] ^ cur[i])){
        break;
      }
    }
    if(i==dep){
      ok[x]--;
      cur[dep] = x;
      res += solve(dep+1);
      ok[x]++;
    }
  }
  return res;
}
int main(){
  int i, j, k;
  mint res;
  wmem = memarr;
  {
    mint x;
    x.setmod(MD);
  }
  comb.init(1100);
  rd(N);
  rd(K);
  rd(X);
  rd(Y);
  {
    int Lj4PdHRW;
    for(Lj4PdHRW=0;Lj4PdHRW<N;Lj4PdHRW++){
      rd(C[Lj4PdHRW]);
    }
  }
  for(i=0;i<K;i++){
    for(j=0;j<K;j++){
      rd(A[i][j]);
    }
  }
  for(i=0;i<K;i++){
    for(j=0;j<K;j++){
      A[i][j] ^= X;
    }
  }
  Y ^= X;
  X = Y;
  for(i=0;i<K;i++){
    for(j=0;j<K;j++){
      A[i][j] = nrm(A[i][j]);
    }
  }
  for(i=0;i<K;i++){
    if(A[i][i] != 0){
      wt_L(0);
      putchar_unlocked('\n');
      return 0;
    }
  }
  for(i=0;i<K;i++){
    for(j=i+1;j<K;j++){
      if(A[i][j] != A[j][i]){
        wt_L(0);
        putchar_unlocked('\n');
        return 0;
      }
    }
  }
  for(i=0;i<2048;i++){
    ok[i] = 0;
  }
  for(i=0;i<2048;i++){
    sz[i][0] = sz[i][1] = 0;
  }
  for(i=0;i<N;i++){
    k = nrm(C[i]);
    ok[k]++;
    if(k==C[i]){
      sz[k][0]++;
    }
    else{
      sz[k][1]++;
    }
  }
  res = solve(0);
  wt_L(res);
  putchar_unlocked('\n');
  return 0;
}
// cLay varsion 20180208-1

// --- original code ---
// int N, K, X, Y, C[2200];
// int A[1100][1100];
// 
// int ok[2200];
// int sz[2200][2];
// 
// int cur[2200];
// int use[2200];
// combination_mint comb;
// 
// inline int nrm(int x){
//   if(x < (x^X)) return x;
//   return x^X;
// }
// 
// mint solve(int dep){
//   int i, j, k, x;
//   mint res, tmp;
//   res = 0;
//   
//   if(dep==K){
//     res = 1;
//     rep(i,2048) use[i] = 0;
//     rep(i,dep) use[cur[i]]++;
//     rep(i,2048) if(use[i]){
//       tmp = 0;
//       rep(j,use[i]+1){
//         if(j <= sz[i][0] && use[i]-j <= sz[i][1]) tmp += comb.C(use[i], j);
//       }
//       res *= tmp;
//     }
//     return res;
//   }
// 
//   if(dep==0){
//     rep(i,2048) if(ok[i]){
//       ok[i]--;
//       cur[dep] = i;
//       res += solve(dep+1);
//       ok[i]++;
//     }
//     return res;
//   }
// 
//   x = nrm(A[0][dep] ^ cur[0]);
//   if(ok[x]){
//     rep(i,dep) if(x != nrm(A[i][dep] ^ cur[i])) break;
//     if(i==dep){
//       ok[x]--;
//       cur[dep] = x;
//       res += solve(dep+1);
//       ok[x]++;
//     }
//   }
//   return res;
// }
// 
// {
//   int i, j, k;
//   mint res;
// 
//   comb.init(1100);
//   
//   rd(N,K,X,Y,C(N));
//   rep(i,K) rep(j,K) rd(A[i][j]);
//   rep(i,K) rep(j,K) A[i][j] ^= X;
//   Y ^= X;
//   X = Y;
// 
//   rep(i,K) rep(j,K) A[i][j] = nrm(A[i][j]);
// 
//   rep(i,K) if(A[i][i] != 0){
//     wt(0); return 0;
//   }
//   rep(i,K) rep(j,i+1,K) if(A[i][j] != A[j][i]){
//     wt(0); return 0;
//   }
// 
//   rep(i,2048) ok[i] = 0;
//   rep(i,2048) sz[i][0] = sz[i][1] = 0;
//   rep(i,N){
//     k = nrm(C[i]);
//     ok[k]++;
//     if(k==C[i]) sz[k][0]++; else sz[k][1]++;
//   }
// 
//   res = solve(0);
//   wt(res);
// }

Submission Info

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