codeforces 623 E FFT

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#include<iostream>#include<algorithm>#include<cstdio>#include<cstdlib>#include<cstring>#include<cmath>using namespace std;typedef long long LL;#define R registerconst int N=66005,P=1000000007,bt=16,mas=65535;const long double _2Pi=2*acos(-1.0);struct na {long double x,y;};inline na operator + (const na &a,const na &b) {return (na){a.x+b.x,a.y+b.y};}inline na operator - (const na &a,const na &b) {return (na){a.x-b.x,a.y-b.y};}inline na operator * (const na &a,const na &b) {return (na){a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x};}//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!inline na conj (const na &a) {return (na){a.x,-a.y};}LL K;int n,m,X,rev[N],fac[N],fr[N],f[N],g[N],ans=0;na ha,w[2][N/2],A[N],B[N],C[N],D[N];inline int pw(int a,int k){int rec=1;for (;k;a=(LL)a*a%P,k>>=1) (k&1)?rec=(LL)rec*a%P:0;return rec;}void FFT(na A[],int r){for (int i=0;i<m;i++) if (i<rev[i]) swap(A[i],A[rev[i]]);for (R int i=1,l=m/2;i<m;i*=2,l>>=1)for (R int j=0;j<m;j+=2*i)for (R int k=0,d=0;k<i;k++,d+=l)ha=A[i+j+k]*w[r][d],A[i+j+k]=A[j+k]-ha,A[j+k]=A[j+k]+ha;if (r) for (int i=0;i<m;i++) A[i].x/=m,A[i].y/=m;}void conv(int f[],int g[],int h[],int len){for (int i=0;i<=n;i++){int a=(LL)f[i]*pw(2,(int)((LL)i*len%(P-1)))%P,b=g[i];A[i]=(na){a>>bt,a&mas};B[i]=(na){b>>bt,b&mas};//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!}for (int i=n+1;i<=m;i++) A[i]=B[i]=(na){0,0};FFT(A,0),FFT(B,0);A[m]=A[0];B[m]=B[0];for (int i=0;i<m;i++){na a1=(A[i]+conj(A[m-i]))*(na){0.5,0},a2=(A[i]-conj(A[m-i]))*(na){0,-0.5};na b1=(B[i]+conj(B[m-i]))*(na){0.5,0},b2=(B[i]-conj(B[m-i]))*(na){0,-0.5};C[i]=a1*b1+(na){0,1}*a2*b2;D[i]=a1*b2+a2*b1;}FFT(C,1),FFT(D,1);for (int i=0;i<=n;i++){int a=(LL)round(C[i].x)%P,b=(LL)round(C[i].y)%P,c=(LL)round(D[i].x)%P;h[i]=(((LL)a<<2*bt)%P+((LL)c<<bt)%P+b)%P;}}int main(){//freopen("1.in","r",stdin);cin>>K>>n;if (K>n) return puts("0"),0;for (m=2,X=1;m<=2*n;m*=2,X++);for (int i=1;i<m;i++) rev[i]=(rev[i>>1]>>1)|((i&1)<<X-1);for (int i=0;i<m/2;i++){long double k=_2Pi*i/m;w[0][i]=(na){cos(k),sin(k)},w[1][i]=(na){cos(-k),sin(-k)};}fac[0]=1;fr[0]=1;for (int i=1;i<=m;i++) fac[i]=(LL)fac[i-1]*i%P,fr[i]=pw(fac[i],P-2);for (int i=1;i<=n;i++) f[i]=fr[i];g[0]=1;for (int x=1;K;K>>=1,x*=2){if (K&1)conv(g,f,g,x);conv(f,f,f,x);}for (int i=0;i<=n;i++) ans=(ans+(LL)g[i]*fac[n]%P*fr[n-i]%P)%P;//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!cout<<ans<<endl;return 0;}
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