LuoguP4593 [TJOI2018]教科书般的亵渎

#include<bits/stdc++.h>
#define Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
#define W while
#define I inline
#define RI register int
#define LL long long
#define Cn const
#define CI Cn int&
#define gc getchar
#define D isdigit(c=gc())
#define pc(c) putchar((c))
#define min(x,y) ((x)<(y)?(x):(y))
#define max(x,y) ((x)>(y)?(x):(y))
using namespace std;
namespace Debug{
    Tp I void _debug(Cn char* f,Ty t){cerr<<f<<'='<<t<<endl;}
    Ts I void _debug(Cn char* f,Ty x,Ar... y){W(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
    Tp ostream& operator<<(ostream& os,Cn vector<Ty>& V){os<<"[";for(Cn auto& vv:V) os<<vv<<",";os<<"]";return os;}
    #define gdb(...) _debug(#__VA_ARGS__,__VA_ARGS__)
}using namespace Debug;
namespace FastIO{
    Tp I void read(Ty& x){char c;int f=1;x=0;W(!D) f=c^'-'?1:-1;W(x=(x<<3)+(x<<1)+(c&15),D);x*=f;}
    Ts I void read(Ty& x,Ar&... y){read(x),read(y...);}
    Tp I void write(Ty x){x<0&&(pc('-'),x=-x,0),x<10?(pc(x+'0'),0):(write(x/10),pc(x%10+'0'),0);}
    Tp I void writeln(Cn Ty& x){write(x),pc('\n');}
}using namespace FastIO;
Cn int N=64+10,P=1e9+7;
int T,m,k,a[N],pre[N],suf[N],ifac[N];
LL n,y,Ans;
I LL QP(LL A,LL B){LL S=1;W(B) B&1&&((S*=A)%=P),(A*=A)%=P,B>>=1;return S;}
int main(){
    RI i,j;ifac[0]=1;for(i=1;i<=57;i++) ifac[i]=1LL*ifac[i-1]*QP(i,P-2)%P;read(T);W(T--){
        for(read(n,m),k=m+1,Ans=0,i=1;i<=m;i++) read(a[i]);for(sort(a+1,a+m+1),i=0;i<=m;i++){
            pre[0]=1;for(j=1;j<=k+2;j++) pre[j]=1LL*pre[j-1]*(n-a[i]-j)%P;
            suf[k+3]=1;for(j=k+2;j;j--) suf[j]=1LL*suf[j+1]*(n-a[i]-j)%P;
            for(y=0,j=1;j<=k+2;j++) (Ans+=1LL*((y+=QP(j,k))%=P)*pre[j-1]%P*suf[j+1]%P*ifac[j-1]%P*ifac[k+2-j]%P*(((k-j)&1)?P-1:1)%P)%=P;
            for(j=i+1;j<=m;j++) (Ans+=P-QP(a[j]-a[i],k))%=P;
        }writeln((Ans+P)%P);
    }return 0;
}