YbtOJ 981「prufer编码」森林之和

#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
#pragma GCC optimize("unroll-loops")
#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&
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{
    #define FS 100000
    #define tc() (FA==FB&&(FB=(FA=FI)+fread(FI,1,FS,stdin),FA==FB)?EOF:*FA++)
    #define pc(c) (FC==FE&&(clear(),0),*FC++=c)
    int OT;char oc,FI[FS],FO[FS],OS[FS],*FA=FI,*FB=FI,*FC=FO,*FE=FO+FS;
    I void clear() {fwrite(FO,1,FC-FO,stdout),FC=FO;}
    Tp I void read(Ty& x) {x=0;RI f=1;W(!isdigit(oc=tc())) f=oc^'-'?1:-1;W(x=(x<<3)+(x<<1)+(oc&15),isdigit(oc=tc()));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);W(OS[++OT]=x%10+48,x/=10);W(OT) pc(OS[OT--]);}
    Tp I void writeln(Ty x) {x<0&&(pc('-'),x=-x);W(OS[++OT]=x%10+48,x/=10);W(OT) pc(OS[OT--]);pc('\n');}
}using namespace FastIO;
Cn int N=5e3+10;
int T,p,n,Ans,fac[N],ifac[N],g[N],f[N],s[N];
I int QP(RI a,RI b){if(b<0) return 0;RI s=1;W(b) b&1&&(s=1LL*s*a%p),a=1LL*a*a%p,b>>=1;return s;}
I int C(CI n,CI m){return n<m?0:1LL*fac[n]*ifac[n-m]%p*ifac[m]%p;}
int main(){
    freopen("forest.in","r",stdin),freopen("forest.out","w",stdout);
    RI i,j,o;read(T,p);for(fac[0]=1,i=1;i<N;i++) fac[i]=1LL*fac[i-1]*i%p;for(ifac[N-1]=QP(fac[N-1],p-2),i=N-2;~i;i--) ifac[i]=1LL*ifac[i+1]*(i+1)%p;
    for(f[1]=1,i=2;i<N;i++) f[i]=QP(i,i-2)%p;
    for(g[0]=1,i=1;i<N;i++) for(j=1;j<=i;j++) g[i]+=1LL*C(i-1,j-1)*g[i-j]%p*f[j]%p,g[i]%=p;
    for(i=2;i<N;i++) for(o=1,j=i-1;j;j--) s[i]+=1LL*C(i-2,j-1)*o%p*j%p*j%p,s[i]%=p,o=1LL*o*(i-1)%p;W(T--){
        for(read(n),Ans=0,i=1;i<=n;i++) Ans+=1LL*C(n-1,i-1)*g[n-i]%p*s[i]%p,Ans%=p;
        writeln(1LL*Ans*n%p);
    }return clear(),0;
}