AGC002 F Leftmost Ball——DP

Topic: https://atcoder.jp/contests/agc002/tasks/agc002_f

Iff prefix number 0> = several colors.

Design DP, put a time to put all the colors of the color points are considered complete, do not put one by one. So do not consider "how much is left of the old color points are available," the.

The new release color when know how many positions have been filled, the number of placement programs in all the color points are counted.

dp [i] [j] denotes the i-th put 0, j color scheme. I think color is put in order, and finally multiplied by the factorial. There \ (dp [i] [j] -> dp [i + 1] [j], dp [i] [j] * \ binom {(nj) (k-1) + ni-1, k-2 } -> dp [i] [j + 1] \).

#include<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long
using namespace std;
const int N=2005,M=N*N,mod=1e9+7;
int upt(int x)
{while(x>=mod)x-=mod;while(x<0)x+=mod;return x;}
int pw(int x,int k)
{int ret=1;while(k){if(k&1)ret=(ll)ret*x%mod;x=(ll)x*x%mod;k>>=1;}return ret;}

int n,k,jc[M],jcn[M],dp[N][N];
void init()
{
  you m = n * k;
  jc[0]=1;for(int i=1;i<=lm;i++)jc[i]=(ll)jc[i-1]*i%mod;
  jcn[lm]=pw(jc[lm],mod-2);
  for(int i=lm-1;i>=0;i--)jcn[i]=(ll)jcn[i+1]*(i+1)%mod;
}
int C(int n,int m)
{
  if(n<0||m<0||n<m)return 0;
  return (ll)jc[n]*jcn[m]%mod*jcn[n-m]%mod;
}
int main ()
{
  scanf("%d%d",&n,&k); if(k==1){puts("1");return 0;}
  init();
  dp[0][0]=1;
  for(int i=0;i<=n;i++)
    for(int j=0;j<=i;j++)
      {
    if(!dp[i][j])continue;int tp=dp[i][j];
    if(i<n)dp[i+1][j]=upt(dp[i+1][j]+tp);
    if(j<i)
      {
        int ml=C((n-j)*(k-1)+n-i-1,k-2);
        dp[i][j+1]=(dp[i][j+1]+(ll)ml*tp)%mod;
      }
      }
  printf("%lld\n",(ll)dp[n][n]*jc[n]%mod);
  return 0;
}