#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');} #define PI 3.141592653589793238462 struct pnt{double x,y;static double eps;pnt(void){}pnt(double a,double b){x=a;y=b;}void set(double a,double b){x=a;y=b;}pnt&operator+=(pnt a){x+=a.x;y+=a.y;return*this;}pnt&operator-=(pnt a){x-=a.x;y-=a.y;return*this;}pnt&operator*=(pnt a){pnt p=*this;x=p.x*a.x-p.y*a.y;y=p.x*a.y+p.y*a.x;return*this;}pnt operator+(pnt a){return pnt(*this)+=a;}pnt operator-(pnt a){return pnt(*this)-=a;}pnt operator*(pnt a){return pnt(*this)*=a;}}; double pnt::eps = 1e-10; void fft(int n, pnt x[], void *mem){int i,j,I,J,K,s=1;double t=2*PI/n,p;pnt w,v,u,a,b,c,d,A,B,C,D,*y=(pnt*)mem;while(n>2){I=n/4;J=I+I;K=I+J;rep(i,I){w=pnt(cos(i*t),-sin(i*t));v=w*w;u=w*v;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,B=a-c,C=b+d,D=b-d,p=D.y,D.y=D.x,D.x=-p,y[j+s*4*i]=A+C,y[j+s*(4*i+1)]=w*(B-D),y[j+s*(4*i+2)]=v*(A-C),y[j+s*(4*i+3)]=u*(B+D);}n/=4;s*=4;t*=4;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;t*=2;swap(x,y);}rep(i,s)y[i]=x[i];} void fftinv(int n, pnt x[], void *mem){int i,j,I,J,K,s=1;double t=2*PI/n,p;pnt w,v,u,a,b,c,d,A,B,C,D,*y=(pnt*)mem;while(n>2){I=n/4;J=I+I;K=I+J;rep(i,I){w=pnt(cos(i*t),sin(i*t));v=w*w;u=w*v;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,B=a-c,C=b+d,D=b-d,p=D.y,D.y=D.x,D.x=-p,y[j+s*4*i]=A+C,y[j+s*(4*i+1)]=w*(B+D),y[j+s*(4*i+2)]=v*(A-C),y[j+s*(4*i+3)]=u*(B-D);}n/=4;s*=4;t*=4;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;t*=2;swap(x,y);}rep(i,s)y[i]=x[i];} void convolution(double A[], int As, double B[], int Bs, double res[], int Rs, void *mem){int i,n,k;double m;pnt*a,*b;n=max(As+Bs,Rs);for(k=1;k