#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');} char memarr[77000000]; void *mem = memarr; #define MD 1004535809 struct mint{ static unsigned md; unsigned a; mint(void){};mint(int n){n%=md;if(n<0)n+=md;a=n;}mint(unsigned n){a=n%md;}mint(ll n){n%=md;if(n<0)n+=md;a=n;}mint(ull n){a=n%md;} mint&operator+=(mint n){a+=n.a;if(a>=md)a-=md;return*this;}mint&operator-=(mint n){if(a>=1;a*=a;}return r;} int get(void){return a;} }; unsigned mint::md = 1004535809; mint mval[10], minv[10]; void mint_init(void){ int i; rep(i,10) mval[i] = i; } void mfft(int n, mint x[], mint root, void *mem){int i,j,X,Y,Z,s=1;mint I,J,K,a,b,c,d,A,B,C,D,t,*y=(mint*)mem;t=root.pw((mint::md-1)/4*3);root=root.pw((mint::md-1)/n);while(n>2){X=n/4;Y=X+X;Z=X+Y;I=1;rep(i,X){J=I*I;K=I*J;rep(j,s)a=x[j+s*i],b=x[j+s*(i+X)],c=x[j+s*(i+Y)],d=x[j+s*(i+Z)],A=a+c,B=a-c,C=b+d,D=(b-d)*t,y[j+s*4*i]=A+C,y[j+s*(4*i+1)]=I*(B-D),y[j+s*(4*i+2)]=J*(A-C),y[j+s*(4*i+3)]=K*(B+D);I*=root;}n/=4;s*=4;root*=root;root*=root;swap(x,y);}if(n==2){rep(i,s)y[i]=x[i]+x[i+s],y[i+s]=x[i]-x[i+s];n/=2;s*=2;root*=root;swap(x,y);}rep(i,s)y[i]=x[i];} void mfftinv(int n, mint x[], mint root, void *mem){int i,j,X,Y,Z,s=1;mint I,J,K,a,b,c,d,A,B,C,D,t,*y=(mint*)mem;root=root.inv();t=root.pw((mint::md-1)/4);root=root.pw((mint::md-1)/n);while(n>2){X=n/4;Y=X+X;Z=X+Y;I=1;rep(i,X){J=I*I;K=I*J;rep(j,s)a=x[j+s*i],b=x[j+s*(i+X)],c=x[j+s*(i+Y)],d=x[j+s*(i+Z)],A=a+c,B=a-c,C=b+d,D=(b-d)*t,y[j+s*4*i]=A+C,y[j+s*(4*i+1)]=I*(B+D),y[j+s*(4*i+2)]=J*(A-C),y[j+s*(4*i+3)]=K*(B-D);I*=root;}n/=4;s*=4;root*=root;root*=root;swap(x,y);}if(n==2){rep(i,s)y[i]=x[i]+x[i+s],y[i+s]=x[i]-x[i+s];n/=2;s*=2;root*=root;swap(x,y);}rep(i,s)y[i]=x[i];} void modconvolution(mint A[], int As, mint B[], int Bs, mint res[], int Rs, void *mem, mint root){int i,n,m;mint*a,*b,r;n=max(As+Bs,Rs);for(m=1;m