結果

問題 No.931 Multiplicative Convolution
コンテスト
ユーザー LayCurse
提出日時 2019-11-22 22:14:55
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 112 ms / 2,000 ms
コード長 16,397 bytes
コンパイル時間 4,108 ms
コンパイル使用メモリ 229,300 KB
最終ジャッジ日時 2025-01-08 05:05:54
ジャッジサーバーID
（参考情報） 		judge2 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 14
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ソースコード

diff # 

#pragma GCC optimize ("Ofast")
#include<bits/stdc++.h>
using namespace std;
#define MD (998244353U)
#define MINT_W (32U)
#define MINT_R (301989884U)
#define MINT_RR (932051910U)
#define MINT_MDNINV (998244351U)
#define MD_PRIMITIVE_ROOT (3U)
#define PI 3.14159265358979323846
void *wmem;
char memarr[96000000];
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{
  unsigned val;
  Mint(){
    val=0;
  }
  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);
  }
  inline unsigned mulR(unsigned a){
    return (unsigned long long)a*MINT_R%MD;
  }
  inline unsigned mulR(int a){
    if(a < 0){
      a = a%((int)MD)+(int)MD;
    }
    return mulR((unsigned)a);
  }
  inline unsigned mulR(unsigned long long a){
    return mulR((unsigned)(a%MD));
  }
  inline unsigned mulR(long long a){
    a %= MD;
    if(a < 0){
      a += MD;
    }
    return mulR((unsigned)a);
  }
  inline unsigned reduce(unsigned T){
    unsigned m = T * MINT_MDNINV;
    unsigned t = (unsigned)((T + (unsigned long long)m*MD) >> MINT_W);
    if(t >= MD){
      t -= MD;
    }
    return t;
  }
  inline unsigned reduce(unsigned long long T){
    unsigned m = (unsigned)T * MINT_MDNINV;
    unsigned t = (unsigned)((T + (unsigned long long)m*MD) >> MINT_W);
    if(t >= MD){
      t -= MD;
    }
    return t;
  }
  inline unsigned get(){
    return reduce(val);
  }
  inline Mint &operator+=(Mint a){
    val += a.val;
    if(val >= MD){
      val -= MD;
    }
    return *this;
  }
  inline Mint &operator-=(Mint a){
    if(val < a.val){
      val = val + MD - a.val;
    }
    else{
      val -= a.val;
    }
    return *this;
  }
  inline Mint &operator*=(Mint a){
    val = reduce((unsigned long long)val*a.val);
    return *this;
  }
  inline Mint &operator/=(Mint a){
    return *this *= a.inverse();
  }
  inline Mint operator+(Mint a){
    return Mint(*this)+=a;
  }
  inline Mint operator-(Mint a){
    return Mint(*this)-=a;
  }
  inline Mint operator*(Mint a){
    return Mint(*this)*=a;
  }
  inline Mint operator/(Mint a){
    return Mint(*this)/=a;
  }
  inline Mint operator+(int a){
    return Mint(*this)+=Mint(a);
  }
  inline Mint operator-(int a){
    return Mint(*this)-=Mint(a);
  }
  inline Mint operator*(int a){
    return Mint(*this)*=Mint(a);
  }
  inline Mint operator/(int a){
    return Mint(*this)/=Mint(a);
  }
  inline Mint operator+(long long a){
    return Mint(*this)+=Mint(a);
  }
  inline Mint operator-(long long a){
    return Mint(*this)-=Mint(a);
  }
  inline Mint operator*(long long a){
    return Mint(*this)*=Mint(a);
  }
  inline Mint operator/(long long a){
    return Mint(*this)/=Mint(a);
  }
  inline Mint operator-(void){
    Mint res;
    if(val){
      res.val=MD-val;
    }
    else{
      res.val=0;
    }
    return res;
  }
  inline operator bool(void){
    return val!=0;
  }
  inline operator int(void){
    return get();
  }
  inline operator long long(void){
    return get();
  }
  inline Mint inverse(){
    int a = val;
    int b = MD;
    int u = 1;
    int v = 0;
    int 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*MINT_RR % MD;
    return res;
  }
  inline Mint pw(unsigned long long b){
    Mint a(*this);
    Mint res;
    res.val = MINT_R;
    while(b){
      if(b&1){
        res *= a;
      }
      b >>= 1;
      a *= a;
    }
    return res;
  }
  inline bool operator==(int a){
    return mulR(a)==val;
  }
  inline bool operator!=(int a){
    return mulR(a)!=val;
  }
}
;
inline Mint operator+(int a, Mint b){
  return Mint(a)+=b;
}
inline Mint operator-(int a, Mint b){
  return Mint(a)-=b;
}
inline Mint operator*(int a, Mint b){
  return Mint(a)*=b;
}
inline Mint operator/(int a, Mint b){
  return Mint(a)/=b;
}
inline Mint operator+(long long a, Mint b){
  return Mint(a)+=b;
}
inline Mint operator-(long long a, Mint b){
  return Mint(a)-=b;
}
inline Mint operator*(long long a, Mint b){
  return Mint(a)*=b;
}
inline Mint operator/(long long a, Mint b){
  return Mint(a)/=b;
}
inline void rd(int &x){
  int k;
  int 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){
  int s=0;
  int m=0;
  char f[10];
  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');
  }
}
template<class T> inline int isPrime_L(T n){
  T i;
  if(n<=1){
    return 0;
  }
  if(n<=3){
    return 1;
  }
  if(n%2==0){
    return 0;
  }
  for(i=3;i*i<=n;i+=2){
    if(n%i==0){
      return 0;
    }
  }
  return 1;
}
template<class T> int Factor_L(T N, T fac[], int fs[]){
  T i;
  int sz = 0;
  if(N%2==0){
    fac[sz] = 2;
    fs[sz] = 1;
    N /= 2;
    while(N%2==0){
      N /= 2;
      fs[sz]++;
    }
    sz++;
  }
  for(i=3;i*i<=N;i+=2){
    if(N%i==0){
      fac[sz] = i;
      fs[sz] = 1;
      N /= i;
      while(N%i==0){
        N /= i;
        fs[sz]++;
      }
      sz++;
    }
  }
  if(N > 1){
    fac[sz] = N;
    fs[sz] = 1;
    sz++;
  }
  return sz;
}
template<class T> int Divisor_L(T N, T res[], void *mem = wmem){
  int i;
  int j;
  int k;
  int s;
  int sz = 0;
  T *fc;
  int *fs;
  int fsz;
  walloc1d(&fc, 100, &mem);
  walloc1d(&fs, 100, &mem);
  fsz =Factor_L(N, fc, fs);
  res[sz++] = 1;
  for(i=(0);i<(fsz);i++){
    s = sz;
    k = s * fs[i];
    for(j=(0);j<(k);j++){
      res[sz++] = res[j] * fc[i];
    }
  }
  sort(res, res+sz);
  return sz;
}
unsigned long long powmod(unsigned long long a, unsigned long long b, unsigned long long m){
  unsigned long long r = 1;
  while(b){
    if(b&1){
      r = r * a % m;
    }
    b>>=1;
    a = a * a % m;
  }
  return r;
}
long long primitiveRoot(long long p, void *mem = wmem){
  int ys;
  long long *y;
  long long r;
  if(!isPrime_L(p)){
    return -1;
  }
  walloc1d(&y, 100000, &mem);
  ys =Divisor_L(p-1, y, mem);
  for(r=(1);r<(p);r++){
    int i;
    for(i=(0);i<(ys-1);i++){
      if(powmod(r,y[i],p) == 1){
        goto OC5CYxKD;
      }
    }
    return r;
    OC5CYxKD:;
  }
  return -1;
}
struct fft_pnt{
  double x;
  double 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){
  int i;
  int j;
  int n1;
  int n2;
  int n3;
  int step = 1;
  double theta = 2*PI / n;
  double tmp;
  fft_pnt w1;
  fft_pnt w2;
  fft_pnt w3;
  fft_pnt a;
  fft_pnt b;
  fft_pnt c;
  fft_pnt d;
  fft_pnt aa;
  fft_pnt bb;
  fft_pnt cc;
  fft_pnt dd;
  fft_pnt *y = (fft_pnt*)mem;
  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){
  int i;
  int j;
  int n1;
  int n2;
  int n3;
  int step = 1;
  double theta = 2*PI / n;
  double tmp;
  fft_pnt w1;
  fft_pnt w2;
  fft_pnt w3;
  fft_pnt a;
  fft_pnt b;
  fft_pnt c;
  fft_pnt d;
  fft_pnt aa;
  fft_pnt bb;
  fft_pnt cc;
  fft_pnt dd;
  fft_pnt *y = (fft_pnt*)mem;
  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){
  int i;
  int n;
  int n2;
  double mul;
  fft_pnt *a;
  fft_pnt *b;
  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);
  }
  int aTt_SmvX = n2;
  for(i=(As);i<(aTt_SmvX);i++){
    a[i].set(0,0);
  }
  for(i=(0);i<(Bs);i++){
    b[i].set(B[i], 0);
  }
  int bXO5jt5I = n2;
  for(i=(Bs);i<(bXO5jt5I);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){
  int i;
  int n;
  int n2;
  double mul;
  fft_pnt *a;
  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);
  }
  int vJNsb2nO = n2;
  for(i=(As);i<(vJNsb2nO);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;
  }
}
void fft_L(int n, Mint x[], Mint root, void *mem){
  int i;
  int j;
  int n1;
  int n2;
  int n3;
  int step = 1;
  Mint w1;
  Mint w2;
  Mint w3;
  Mint a;
  Mint b;
  Mint c;
  Mint d;
  Mint aa;
  Mint bb;
  Mint cc;
  Mint dd;
  Mint tmp;
  Mint *y;
  walloc1d(&y, n, &mem);
  tmp = root.pw((MD-1)/4*3);
  root = root.pw((MD-1)/n);
  while(n > 2){
    n1 = n / 4;
    n2 = n1 + n1;
    n3 = n1 + n2;
    w1.val = MINT_R;
    for(i=(0);i<(n1);i++){
      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;
        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);
      }
      w1 *= root;
    }
    n /= 4;
    step *= 4;
    root *= root;
    root *= root;
    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;
    root *= root;
    swap(x,y);
  }
  for(i=(0);i<(step);i++){
    y[i] = x[i];
  }
}
void fftinv_L(int n, Mint x[], Mint root, void *mem){
  int i;
  int j;
  int n1;
  int n2;
  int n3;
  int step = 1;
  Mint w1;
  Mint w2;
  Mint w3;
  Mint a;
  Mint b;
  Mint c;
  Mint d;
  Mint aa;
  Mint bb;
  Mint cc;
  Mint dd;
  Mint tmp;
  Mint *y;
  walloc1d(&y, n, &mem);
  root = root.inverse();
  tmp = root.pw((MD-1)/4);
  root = root.pw((MD-1)/n);
  while(n > 2){
    n1 = n / 4;
    n2 = n1 + n1;
    n3 = n1 + n2;
    w1.val = MINT_R;
    for(i=(0);i<(n1);i++){
      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;
        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);
      }
      w1 *= root;
    }
    n /= 4;
    step *= 4;
    root *= root;
    root *= root;
    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;
    root *= root;
    swap(x,y);
  }
  for(i=(0);i<(step);i++){
    y[i] = x[i];
  }
}
void convolution_L(Mint A[], int As, Mint B[], int Bs, Mint res[], int Rs,  Mint root = MD_PRIMITIVE_ROOT, void *mem = wmem){
  int i;
  int n;
  int n2;
  Mint *a;
  Mint *b;
  Mint r;
  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] = A[i];
  }
  int U5xJbqP4 = n2;
  for(i=(As);i<(U5xJbqP4);i++){
    a[i].val = 0;
  }
  for(i=(0);i<(Bs);i++){
    b[i] = B[i];
  }
  int dDIyew82 = n2;
  for(i=(Bs);i<(dDIyew82);i++){
    b[i].val = 0;
  }
  fft_L(n2, a, root, mem);
  fft_L(n2, b, root, mem);
  for(i=(0);i<(n2);i++){
    a[i] *= b[i];
  }
  fftinv_L(n2, a, root, mem);
  r = Mint(n2).inverse();
  for(i=(0);i<(Rs);i++){
    res[i] = a[i] * r;
  }
}
void convolution_L(Mint A[], int As, Mint res[], int Rs, Mint root = MD_PRIMITIVE_ROOT, void *mem = wmem){
  int i;
  int n;
  int n2;
  Mint *a;
  Mint r;
  n =max_L(2*As, Rs);
  for(n2=1;n2<n;n2*=2){
    ;
  }
  walloc1d(&a, n2, &mem);
  for(i=(0);i<(As);i++){
    a[i] = A[i];
  }
  int m7of8KOo = n2;
  for(i=(As);i<(m7of8KOo);i++){
    a[i].val = 0;
  }
  fft_L(n2, a, root, mem);
  for(i=(0);i<(n2);i++){
    a[i] *= a[i];
  }
  fftinv_L(n2, a, root, mem);
  r = Mint(n2).inverse();
  for(i=(0);i<(Rs);i++){
    res[i] = a[i]*r;
  }
}
int P;
int A[100000];
int B[100000];
int c[100000];
Mint x[100000];
Mint y[100000];
Mint z[200000];
int main(){
  wmem = memarr;
  int i;
  int j;
  int k;
  int r;
  rd(P);
  {
    int Lj4PdHRW;
    for(Lj4PdHRW=(0);Lj4PdHRW<(P-1);Lj4PdHRW++){
      rd(A[Lj4PdHRW]);
    }
  }
  {
    int e98WHCEY;
    for(e98WHCEY=(0);e98WHCEY<(P-1);e98WHCEY++){
      rd(B[e98WHCEY]);
    }
  }
  r = primitiveRoot(P);
  for(i=(0);i<(P-1);i++){
    k = powmod(r,i,P);
    x[i] = A[k-1];
    y[i] = B[k-1];
  }
  convolution_L(x,P-1,y,P-1,z,2*P-2);
  for(i=(0);i<(P-1);i++){
    k = powmod(r,i,P);
    c[k-1] = z[i] + z[i+P-1];
  }
  {
    int KrdatlYV;
    if(P-1==0){
      putchar_unlocked('\n');
    }
    else{
      for(KrdatlYV=(0);KrdatlYV<(P-1-1);KrdatlYV++){
        wt_L(c[KrdatlYV]);
        wt_L(' ');
      }
      wt_L(c[KrdatlYV]);
      wt_L('\n');
    }
  }
  return 0;
}
// cLay varsion 20191122-1 [beta]

// --- original code ---
// #define MD 998244353
// int P, A[1d5], B[1d5], c[1d5];
// Mint x[1d5], y[1d5], z[2d5];
// {
//   int i, j, k, r;
//   rd(P,A(P-1),B(P-1));
//   r = primitiveRoot(P);
//   rep(i,P-1){
//     k = powmod(r,i,P);
//     x[i] = A[k-1];
//     y[i] = B[k-1];
//   }
//   convolution(x,P-1,y,P-1,z,2*P-2);
//   rep(i,P-1){
//     k = powmod(r,i,P);
//     c[k-1] = z[i] + z[i+P-1];
//   }
//   wt(c(P-1));
// }
0