結果

問題 No.1239 Multiplication -2
ユーザー LayCurse
提出日時 2020-09-25 21:56:30
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 17,668 bytes
コンパイル時間 2,573 ms
コンパイル使用メモリ 227,748 KB
最終ジャッジ日時 2025-01-14 20:55:06
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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 * 10 WA * 24
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ソースコード

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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 (998244353U)
#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 Modint{
  unsigned val;
  Modint(){
    val=0;
  }
  Modint(int a){
    val = ord(a);
  }
  Modint(unsigned a){
    val = ord(a);
  }
  Modint(long long a){
    val = ord(a);
  }
  Modint(unsigned long long a){
    val = ord(a);
  }
  inline unsigned ord(unsigned a){
    return a%MD;
  }
  inline unsigned ord(int a){
    a %= (int)MD;
    if(a < 0){
      a += MD;
    }
    return a;
  }
  inline unsigned ord(unsigned long long a){
    return a%MD;
  }
  inline unsigned ord(long long a){
    a %= (int)MD;
    if(a < 0){
      a += MD;
    }
    return a;
  }
  inline unsigned get(){
    return val;
  }
  inline Modint &operator+=(Modint a){
    val += a.val;
    if(val >= MD){
      val -= MD;
    }
    return *this;
  }
  inline Modint &operator-=(Modint a){
    if(val < a.val){
      val = val + MD - a.val;
    }
    else{
      val -= a.val;
    }
    return *this;
  }
  inline Modint &operator*=(Modint a){
    val = ((unsigned long long)val*a.val)%MD;
    return *this;
  }
  inline Modint &operator/=(Modint a){
    return *this *= a.inverse();
  }
  inline Modint operator+(Modint a){
    return Modint(*this)+=a;
  }
  inline Modint operator-(Modint a){
    return Modint(*this)-=a;
  }
  inline Modint operator*(Modint a){
    return Modint(*this)*=a;
  }
  inline Modint operator/(Modint a){
    return Modint(*this)/=a;
  }
  inline Modint operator+(int a){
    return Modint(*this)+=Modint(a);
  }
  inline Modint operator-(int a){
    return Modint(*this)-=Modint(a);
  }
  inline Modint operator*(int a){
    return Modint(*this)*=Modint(a);
  }
  inline Modint operator/(int a){
    return Modint(*this)/=Modint(a);
  }
  inline Modint operator+(long long a){
    return Modint(*this)+=Modint(a);
  }
  inline Modint operator-(long long a){
    return Modint(*this)-=Modint(a);
  }
  inline Modint operator*(long long a){
    return Modint(*this)*=Modint(a);
  }
  inline Modint operator/(long long a){
    return Modint(*this)/=Modint(a);
  }
  inline Modint operator-(void){
    Modint 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 Modint inverse(){
    int a = val;
    int b = MD;
    int u = 1;
    int v = 0;
    int t;
    Modint 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 = u;
    return res;
  }
  inline Modint pw(unsigned long long b){
    Modint a(*this);
    Modint res;
    res.val = 1;
    while(b){
      if(b&1){
        res *= a;
      }
      b >>= 1;
      a *= a;
    }
    return res;
  }
  inline bool operator==(int a){
    return ord(a)==val;
  }
  inline bool operator!=(int a){
    return ord(a)!=val;
  }
}
;
inline Modint operator+(int a, Modint b){
  return Modint(a)+=b;
}
inline Modint operator-(int a, Modint b){
  return Modint(a)-=b;
}
inline Modint operator*(int a, Modint b){
  return Modint(a)*=b;
}
inline Modint operator/(int a, Modint b){
  return Modint(a)/=b;
}
inline Modint operator+(long long a, Modint b){
  return Modint(a)+=b;
}
inline Modint operator-(long long a, Modint b){
  return Modint(a)-=b;
}
inline Modint operator*(long long a, Modint b){
  return Modint(a)*=b;
}
inline Modint operator/(long long a, Modint b){
  return Modint(a)/=b;
}
inline int my_getchar_unlocked(){
  static char buf[1048576];
  static int s = 1048576;
  static int e = 1048576;
  if(s == e && e == 1048576){
    e = fread_unlocked(buf, 1, 1048576, stdin);
    s = 0;
  }
  if(s == e){
    return EOF;
  }
  return buf[s++];
}
inline void rd(int &x){
  int k;
  int m=0;
  x=0;
  for(;;){
    k = my_getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = my_getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
struct MY_WRITER{
  char buf[1048576];
  int s;
  int e;
  MY_WRITER(){
    s = 0;
    e = 1048576;
  }
  ~MY_WRITER(){
    if(s){
      fwrite_unlocked(buf, 1, s, stdout);
    }
  }
}
;
MY_WRITER MY_WRITER_VAR;
void my_putchar_unlocked(int a){
  if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){
    fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout);
    MY_WRITER_VAR.s = 0;
  }
  MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a;
}
inline void wt_L(char a){
  my_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){
    my_putchar_unlocked('-');
  }
  while(s--){
    my_putchar_unlocked(f[s]+'0');
  }
}
inline void wt_L(Modint 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;
  for(;;){
    if(b&1){
      res *= a;
    }
    b >>= 1;
    if(b==0){
      break;
    }
    a *= a;
  }
  return res;
}
inline double pow_L(double a, double b){
  return pow(a,b);
}
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 KaFyNJB9 = n2;
  for(i=(As);i<(KaFyNJB9);i++){
    a[i].set(0,0);
  }
  for(i=(0);i<(Bs);i++){
    b[i].set(B[i], 0);
  }
  int jO2HaRTX = n2;
  for(i=(Bs);i<(jO2HaRTX);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 eNrGll8F = n2;
  for(i=(As);i<(eNrGll8F);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, Modint x[], Modint root, void *mem){
  int i;
  int j;
  int n1;
  int n2;
  int n3;
  int step = 1;
  Modint w1;
  Modint w2;
  Modint w3;
  Modint a;
  Modint b;
  Modint c;
  Modint d;
  Modint aa;
  Modint bb;
  Modint cc;
  Modint dd;
  Modint tmp;
  Modint*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 = 1;
    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, Modint x[], Modint root, void *mem){
  int i;
  int j;
  int n1;
  int n2;
  int n3;
  int step = 1;
  Modint w1;
  Modint w2;
  Modint w3;
  Modint a;
  Modint b;
  Modint c;
  Modint d;
  Modint aa;
  Modint bb;
  Modint cc;
  Modint dd;
  Modint tmp;
  Modint*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 = 1;
    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(Modint A[], int As, Modint B[], int Bs, Modint res[], int Rs,  Modint root = MD_PRIMITIVE_ROOT, void *mem = wmem){
  int i;
  int n;
  int n2;
  Modint*a;
  Modint*b;
  Modint 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 CnS5KYSU = n2;
  for(i=(As);i<(CnS5KYSU);i++){
    a[i].val = 0;
  }
  for(i=(0);i<(Bs);i++){
    b[i] = B[i];
  }
  int YtJecZqT = n2;
  for(i=(Bs);i<(YtJecZqT);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 = Modint(n2).inverse();
  for(i=(0);i<(Rs);i++){
    res[i] = a[i] * r;
  }
}
void convolution_L(Modint A[], int As, Modint res[], int Rs, Modint root = MD_PRIMITIVE_ROOT, void *mem = wmem){
  int i;
  int n;
  int n2;
  Modint*a;
  Modint 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 jIDgiLP1 = n2;
  for(i=(As);i<(jIDgiLP1);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 = Modint(n2).inverse();
  for(i=(0);i<(Rs);i++){
    res[i] = a[i]*r;
  }
}
int N;
int A[200000];
int ls;
Modint lp[200000+1];
Modint lm[200000+1];
int rs;
Modint rp[200000+1];
Modint rm[200000+1];
Modint c1[200000+1];
Modint c2[200000+1];
int main(){
  wmem = memarr;
  int i;
  int j;
  int k;
  int ad;
  Modint res = 0;
  rd(N);
  {
    int Lj4PdHRW;
    for(Lj4PdHRW=(0);Lj4PdHRW<(N);Lj4PdHRW++){
      rd(A[Lj4PdHRW]);
    }
  }
  for(i=(0);i<(N);i++){
    if(A[i]==2 || A[i]==-2){
      ls = 1;
      lp[0] = 1;
      lm[0] = 0;
      j = i;
      for(;;){
        j--;
        if(j < 0 || A[j] == 0 || A[j] == 2 || A[j] == -2){
          break;
        }
        lp[ls] = lp[ls-1];
        lm[ls] = lm[ls-1];
        if(A[j]==-1){
          swap(lp[ls], lm[ls]);
        }
        ls++;
      }
      if(ls > 1 && j==-1){
        lp[ls-2] += lp[ls-1];
        lm[ls-2] += lm[ls-1];
        ls--;
      }
      rs = 1;
      rp[0] = 1;
      rm[0] = 0;
      j = i;
      for(;;){
        j++;
        if(j >= N || A[j] == 0 || A[j] == 2 || A[j] == -2){
          break;
        }
        rp[ls] = rp[rs-1];
        rm[ls] = rm[rs-1];
        if(A[j]==-1){
          swap(rp[ls], rm[ls]);
        }
        rs++;
      }
      if(rs > 1 && j==N){
        rp[ls-2] += rp[rs-1];
        rm[ls-2] += rm[rs-1];
        rs--;
      }
      if(A[i]==2){
        convolution_L(lp, ls, rm, rs, c1, ls+rs);
        convolution_L(lm, ls, rp, rs, c2, ls+rs);
      }
      else{
        convolution_L(lp, ls, rp, rs, c1, ls+rs);
        convolution_L(lm, ls, rm, rs, c2, ls+rs);
      }
      ad = 0;
      if(i==0){
        ad++;
      }
      if(i==N-1){
        ad++;
      }
      for(k=(0);k<(ls+rs);k++){
        c1[k] += c2[k];
      }
      for(k=(0);k<(ls+rs);k++){
        if(c1[k] != 0){
          res += c1[k] * ((pow_L(Modint(2),(N-3-k+ad))));
        }
      }
    }
  }
  res /=(pow_L(Modint(2),(N - 1)));
  wt_L(res);
  wt_L('\n');
  return 0;
}
// cLay varsion 20200920-1
// --- original code ---
// #define MD 998244353
// int N, A[2d5];
// 
// int ls; Modint lp[2d5+1], lm[2d5+1];
// int rs; Modint rp[2d5+1], rm[2d5+1];
// Modint c1[2d5+1], c2[2d5+1];
// 
// {
//   int i, j, k, ad;
//   Modint res = 0;
//   rd(N,A(N));
// 
//   rep(i,N) if(A[i]==2 || A[i]==-2){
//     ls = 1;
//     lp[0] = 1; lm[0] = 0;
//     j = i;
//     for(;;){
//       j--;
//       if(j < 0 || A[j] == 0 || A[j] == 2 || A[j] == -2) break;
//       lp[ls] = lp[ls-1];
//       lm[ls] = lm[ls-1];
//       if(A[j]==-1) swap(lp[ls], lm[ls]);
//       ls++;
//     }
//     if(ls > 1 && j==-1){
//       lp[ls-2] += lp[ls-1];
//       lm[ls-2] += lm[ls-1];
//       ls--;
//     }
// 
//     rs = 1;
//     rp[0] = 1; rm[0] = 0;
//     j = i;
//     for(;;){
//       j++;
//       if(j >= N || A[j] == 0 || A[j] == 2 || A[j] == -2) break;
//       rp[ls] = rp[rs-1];
//       rm[ls] = rm[rs-1];
//       if(A[j]==-1) swap(rp[ls], rm[ls]);
//       rs++;
//     }
//     if(rs > 1 && j==N){
//       rp[ls-2] += rp[rs-1];
//       rm[ls-2] += rm[rs-1];
//       rs--;
//     }
// 
//     //wt("i = ", i, A[i]);
//     //wt("lp", lp(ls));
//     //wt("lm", lm(ls));
//     //wt("rp", rp(rs));
//     //wt("rm", rm(rs));
// 
//     if(A[i]==2){
//       convolution(lp, ls, rm, rs, c1, ls+rs);
//       convolution(lm, ls, rp, rs, c2, ls+rs);
//     } else {
//       convolution(lp, ls, rp, rs, c1, ls+rs);
//       convolution(lm, ls, rm, rs, c2, ls+rs);
//     }
// 
//     ad = 0;
//     if(i==0) ad++;
//     if(i==N-1) ad++;
// 
//     rep(k,ls+rs) c1[k] += c2[k];
//     //wt("c", c1(ls+rs));
//     rep(k,ls+rs) if(c1[k] != 0){
//       res += c1[k] * (Modint(2) ** (N-3-k+ad));
//     }
//     //wt("res", res);
//   }
// 
//   res /= Modint(2) ** (N - 1);
//   wt(res);
// }
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