[LOJ#3119][Luogu5400][CTS2019]随机立方体(容斥+DP)

https://www.cnblogs.com/cjyyb/p/10900993.html

 #include<cstdio>
 #include<algorithm>
 #define rep(i,l,r) for (int i=(l); i<=(r); i++)
 using namespace std;

 const int N=,mod=;
 int n,m,l,d,V,M,k,T,ans,v[N],w[N],s[N],is[N],fac[N],inv[N];

 int C(int n,int m){ return n<m ?  : 1ll*fac[n]*inv[m]%mod*inv[n-m]%mod; }

 int ksm(int a,int b){
     int res=;
     for (; b; a=1ll*a*a%mod,b>>=)
         if (b & ) res=1ll*res*a%mod;
     return res;
 }

 void init(int n){
     fac[]=; rep(i,,n) fac[i]=1ll*fac[i-]*i%mod;
     inv[n]=ksm(fac[n],mod-); for (int i=n; i; i--) inv[i-]=1ll*inv[i]*i%mod;
 }

 int main(){
     freopen("cube.in","r",stdin);
     freopen("cube.out","w",stdout);
     init(N-);
     for (scanf("%d",&T); T--; ){
         scanf("%d%d%d%d",&n,&m,&l,&k); V=1ll*n*m%mod*l%mod; M=min(min(n,m),l); ans=; d=;
         rep(i,,M) v[i]=(V-1ll*(n-i)*(m-i)%mod*(l-i)%mod+mod)%mod;
         rep(i,,M) w[i]=1ll*C(n,i)*C(m,i)%mod*C(l,i)%mod*fac[i]%mod*fac[i]%mod*fac[i]%mod;
         s[]=; rep(i,,M) s[i]=1ll*s[i-]*v[i]%mod;
         is[M]=ksm(s[M],mod-); for (int i=M; i; i--) is[i-]=1ll*is[i]*v[i]%mod;
         rep(i,k,M) ans=(ans+1ll*d*C(i,k)%mod*w[i]%mod*is[i])%mod,d=mod-d;
         printf("%d\n",ans);
     }
     return ;
 }