FFT

  void FFT(complex a[],int n,int fl){
      for (int i=,j=n/;i<n;i++){
        if (i<j) {complex t=a[i];a[i]=a[j];a[j]=t;};
        int k;
      for (k=(n>>);j&k;j^=k,k>>=);
      j^=k;
    }

     for (int i=;i<=n;i<<=){
      complex w;w.r=cos(fl**pi/i);w.i=sin(fl**pi/i);
      for (int j=;j<n;j+=i){
          complex wi;wi.r=;wi.i=;
          for (int k=j;k<j+i/;k++){
            complex u=a[k],v=a[k+i/]*wi;
          a[k]=u+v;a[k+i/]=u-v;
          wi=wi*w;
        }
      }
    }

    if (fl==-) for (int i=;i<n;i++) a[i].r/=n;
  }

fl==1求点值 fl==-1插值

_________________________
DFT

void DFT(){
  for (int i=;i<n;i++){
      cp t=(cp){cos(*pi/n*i),sin(*pi/n*i)},bas=(cp){,};
      for (int j=;j<n;j++){
        tmp[i]=tmp[i]+bas*a[j];
      bas=bas*t;
    }
  }
  for (int i=;i<n;i++) a[i]=tmp[i];
}

void IDFT(){
  for (int i=;i<n;i++) P[i].r=P[i].i=;
  for (int i=;i<n;i++){
      cp t=(cp){cos(-*pi/n*i),sin(-*pi/n*i)},bas=(cp){,};
    for (int j=;j<n;j++){
      P[i]=P[i]+tmp[j]*bas;
      bas=bas*t;
    }
  }    

  for (int i=;i<n;i++) P[i].r=(int)(P[i].r/n+0.5);
}

-------------------------------------------------------------------------

CODECHEF JUNE15 MOREFB

系数为多项式的分治FFT

#include <bits/stdc++.h>
#define LL long long
#define LDB long double
using namespace std;

  const LDB pi=acos(-);
  const LL mo=;

  int a[],n,k;

  struct data{
      LL a_1,a_n;
  };

  inline data operator*(data a,data b) {return((data){(a.a_n*b.a_n+a.a_1*b.a_1)%mo,(a.a_n*b.a_n+a.a_1*b.a_n+a.a_n*b.a_1)%mo});};

  struct cp{
      LDB r_1,r_n,r_n2,i_1,i_n,i_n2;

      void set0(){
        r_1=r_n=r_n2=i_1=i_n=i_n2=;
    }

    void set(data a){
      set0();
      r_1=a.a_1;r_n=a.a_n;
    }
  }A[],B[];

  inline cp operator *(cp a,cp b){
      return((cp)
      {
          a.r_1*b.r_1-a.i_1*b.i_1,
          a.r_n*b.r_1+a.r_1*b.r_n-a.i_n*b.i_1-a.i_1*b.i_n,
          a.r_n2*b.r_1+a.r_n*b.r_n+a.r_1*b.r_n2-a.i_n2*b.i_1-a.i_n*b.i_n-a.i_1*b.i_n2,
          a.r_1*b.i_1+a.i_1*b.r_1,
          a.r_n*b.i_1+a.r_1*b.i_n+a.i_n*b.r_1+a.i_1*b.r_n,
          a.r_n2*b.i_1+a.r_n*b.i_n+a.r_1*b.i_n2+a.i_n2*b.r_1+a.i_n*b.r_n+a.i_1*b.r_n2
      });
  }

  inline cp operator +(cp a,cp b){
      return((cp)
      {
          a.r_1+b.r_1,
          a.r_n+b.r_n,
          a.r_n2+b.r_n2,
          a.i_1+b.i_1,
          a.i_n+b.i_n,
          a.i_n2+b.i_n2,
      });
  }

  inline cp operator -(cp a,cp b){
      return((cp)
      {
          a.r_1-b.r_1,
          a.r_n-b.r_n,
          a.r_n2-b.r_n2,
          a.i_1-b.i_1,
          a.i_n-b.i_n,
          a.i_n2-b.i_n2,
      });
  }

  data getkth(int po){
      data ret;ret.a_1=;ret.a_n=;
      data bas;bas.a_1=;bas.a_n=;
      for (;po;bas=bas*bas){
        if (po&) ret=ret*bas;
      po>>=;
    }
    return(ret);
  }

   void FFT(cp a[],int n,int fl){
    for (int i=,j=n/;i<n;i++){
      if (i<j) {cp t=a[i];a[i]=a[j];a[j]=t;};
      int k;
      for (k=(n>>);j&k;j^=k,k>>=);
      j^=k;
    }

     for (int i=;i<=n;i<<=){
      cp w;w.set0();
      w.r_1=cos(fl**pi/i);w.i_1=sin(fl**pi/i);
      for (int j=;j<n;j+=i){
        cp wi;wi.set0();
        wi.r_1=;wi.i_1=;
        for (int k=j;k<j+i/;k++){
          cp u=a[k],v=a[k+i/]*wi;
          a[k]=u+v;a[k+i/]=u-v;
          wi=wi*w;
        }
      }
    }

    if (fl==-) for (int i=;i<n;i++) a[i].r_n2/=n,a[i].r_n/=n,a[i].r_1/=n;
  }
  vector <data> MUL(vector <data> &a,vector <data> &b){
      int n=;
      while (n<a.size()+b.size()) n<<=;
      for (int i=;i<n;i++){
        if (i<a.size()) A[i].set(a[i]);else A[i].set0();
      if (i<b.size()) B[i].set(b[i]);else B[i].set0();
    }

    FFT(A,n,);FFT(B,n,);
    for (int i=;i<n;i++) A[i]=A[i]*B[i];
    FFT(A,n,-);

    vector <data> ret;ret.resize(a.size()+b.size());
    for (int i=;i<a.size()+b.size();i++){
      LL tn2=(A[i].r_n2+0.5),tn=(A[i].r_n+0.5),t1=(A[i].r_1+0.5);
      ret[i].a_n=(tn2+tn)%mo;ret[i].a_1=(tn2+t1)%mo;
    }
    return(ret);
  }

  void show(vector <data> tmp1,vector <data> tmp2){
      for (int i=;i<tmp1.size();i++) printf("%lld %lld|",tmp1[i].a_n,tmp1[i].a_1);printf("\n");
      for (int i=;i<tmp2.size();i++) printf("%lld %lld|",tmp2[i].a_n,tmp2[i].a_1);printf("\n");
      vector <data> res=MUL(tmp1,tmp2);
      for (int i=;i<res.size();i++) printf("%lld %lld|",res[i].a_n,res[i].a_1);printf("\n\n");
  }

  vector <data> solve(int l,int r){
      if (l==r){
        vector <data> ret;ret.resize();
      ret[].a_1=;ret[].a_n=;
      ret[]=getkth(a[l]);
      return(ret);
    }

    int mid=(l+r)>>;
    vector <data> tmp1=solve(l,mid);
    vector <data> tmp2=solve(mid+,r);
//    show(tmp1,tmp2);
    return(MUL(tmp1,tmp2));
  }

  int main(){
      scanf("%d%d",&n,&k);
      for (int i=;i<=n;i++) scanf("%d",&a[i]);
      vector <data> ans=solve(,n);
      printf("%lld\n",ans[k].a_n%mo);
  }