#include using namespace std; #define REP(i,a,b) for(i=a;i'9')break;*x=(*x)*10+k-'0';}if(m)(*x)=-(*x);} void reader(ll *x){int k,m=0;*x=0;for(;;){mygc(k);if(k=='-'){m=1;break;}if('0'<=k&&k<='9'){*x=k-'0';break;}}for(;;){mygc(k);if(k<'0'||k>'9')break;*x=(*x)*10+k-'0';}if(m)(*x)=-(*x);} void reader(double *x){scanf("%lf",x);} int reader(char c[]){int i,s=0;for(;;){mygc(i);if(i!=' '&&i!='\n'&&i!='\r'&&i!='\t'&&i!=EOF) break;}c[s++]=i;for(;;){mygc(i);if(i==' '||i=='\n'||i=='\r'||i=='\t'||i==EOF) break;c[s++]=i;}c[s]='\0';return s;} template void reader(T *x, S *y){reader(x);reader(y);} template void reader(T *x, S *y, U *z){reader(x);reader(y);reader(z);} template void reader(T *x, S *y, U *z, V *w){reader(x);reader(y);reader(z);reader(w);} void writer(int x, char c){int s=0,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)mypc('-');while(s--)mypc(f[s]+'0');mypc(c);} void writer(ll x, char c){int s=0,m=0;char f[20];if(x<0)m=1,x=-x;while(x)f[s++]=x%10,x/=10;if(!s)f[s++]=0;if(m)mypc('-');while(s--)mypc(f[s]+'0');mypc(c);} void writer(double x, char c){printf("%.15f",x);mypc(c);} void writer(const char c[]){int i;for(i=0;c[i]!='\0';i++)mypc(c[i]);} void writer(const char x[], char c){int i;for(i=0;x[i]!='\0';i++)mypc(x[i]);mypc(c);} template void writerLn(T x){writer(x,'\n');} template void writerLn(T x, S y){writer(x,' ');writer(y,'\n');} template void writerLn(T x, S y, U z){writer(x,' ');writer(y,' ');writer(z,'\n');} template void writerArr(T x[], int n){int i;if(!n){mypc('\n');return;}rep(i,n-1)writer(x[i],' ');writer(x[n-1],'\n');} ull pw(ull a, ull b, ull m){ull r=1;while(b){if(b&1)r=r*a%m;b>>=1;a=a*a%m;}return r;} int get_inv(ll a, int md){ll t=a,s=md,u=1,v=0,e;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 mfft(int n, int x[], int root, int md, void *mem){int i,j,I,J,K,s=1,p,w,v,u,a,b,c,d,A,B,C,D,*y=(int*)mem;p=pw(root,(md-1)/4*3,md);root=pw(root,(md-1)/n,md);while(n>2){I=n/4;J=I+I;K=I+J;w=1;rep(i,I){v=(ll)w*w%md;u=(ll)w*v%md;rep(j,s){a=x[j+s*i];b=x[j+s*(i+I)];c=x[j+s*(i+J)];d=x[j+s*(i+K)];A=a+c;if(A>=md)A-=md;B=a-c;if(B<0)B+=md;C=b+d;if(C>=md)C-=md;D=b-d;if(D<0)D+=md;D=(ll)D*p%md;y[j+s*4*i]=A+C;y[j+s*(4*i+1)]=(ll)w*(B-D)%md;y[j+s*(4*i+2)]=(ll)v*(A-C)%md;y[j+s*(4*i+3)]=(ll)u*(B+D)%md;if(y[j+s*4*i]>=md)y[j+s*4*i]-=md;if(y[j+s*(4*i+1)]<0)y[j+s*(4*i+1)]+=md;if(y[j+s*(4*i+2)]<0)y[j+s*(4*i+2)]+=md;}w = (ll)w*root%md;}n/=4;s*=4;root=(ll)root*root%md;root=(ll)root*root%md;swap(x,y);}if(n==2){rep(i,s){y[i]=x[i]+x[i+s];if(y[i]>=md)y[i]-=md;y[i+s]=x[i]-x[i+s];if(y[i+s]<0)y[i+s]+=md;}n/=2;s*=2;root=(ll)root*root%md;swap(x,y);}rep(i,s)y[i]=x[i];} void mfftinv(int n, int x[], int root, int md, void *mem){int i,j,I,J,K,s=1,p,w,v,u,a,b,c,d,A,B,C,D,*y=(int*)mem;root=get_inv(root,md);p=pw(root,(md-1)/4,md);root=pw(root,(md-1)/n,md);while(n>2){I=n/4;J=I+I;K=I+J;w=1;rep(i,I){v=(ll)w*w%md;u=(ll)w*v%md;rep(j,s){a=x[j+s*i];b=x[j+s*(i+I)];c=x[j+s*(i+J)];d=x[j+s*(i+K)];A=a+c;if(A>=md)A-=md;B=a-c;if(B<0)B+=md;C=b+d;if(C>=md)C-=md;D=b-d;if(D<0)D+=md;D=(ll)D*p%md;y[j+s*4*i]=A+C;y[j+s*(4*i+1)]=(ll)w*(B+D)%md;y[j+s*(4*i+2)]=(ll)v*(A-C)%md;y[j+s*(4*i+3)]=(ll)u*(B-D)%md;if(y[j+s*4*i]>=md)y[j+s*4*i]-=md;if(y[j+s*(4*i+2)]<0)y[j+s*(4*i+2)]+=md;if(y[j+s*(4*i+3)]<0)y[j+s*(4*i+3)]+=md;}w=(ll)w*root%md;}n/=4;s*=4;root=(ll)root*root%md;root=(ll)root*root%md;swap(x,y);}if(n==2){rep(i,s){y[i]=x[i]+x[i+s];if(y[i]>=md)y[i]-=md;y[i+s]=x[i]-x[i+s];if(y[i+s]<0)y[i+s]+=md;}n/=2;s*=2;root=(ll)root*root%md;swap(x,y);}rep(i,s)y[i]=x[i];} template void modconvolution(S A[], int As, T B[], int Bs, U res[], int Rs, void *mem, int md, int root, int ordered=1){int i,n,k,r,*a,*b;n=max(As+Bs,Rs);for(k=1;k void modconvolution(S A[], int As, T res[], int Rs, void *mem, int md, int root, int ordered=1){int i,n,k,r,*a;n=max(2*As,Rs);for(k=1;k