Problem: Snuke loves colorful balls. He has a total of N×K balls, K in each of his favorite N colors. The colors are numbered 1 through N.

He will arrange all of the balls in a row from left to right, in arbitrary order. Then, for each of the N colors, he will paint the leftmost ball of that color into color 0, a color different from any of the N original colors.

After painting, how many sequences of the colors of the balls are possible? Find this number modulo 10^9+7.

Constraints

* 1≤N,K≤2,000

Input

The input is given from Standard Input in the following format:


N K


Output

Print the number of the possible sequences of the colors of the balls after painting, modulo 10^9+7.

Examples

Input

2 2


Output

4


Input

3 1


Output

1


Input

2 3


Output

14


Input

2000 2000


Output

546381702

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
const int N=2e3+7,p=1e9+7;
int n,k,dp[N][N]; long long fac[N*N],ifac[N*N];
inline int pows(long long u,int v){
	long long ans=1; while(v>0) {if(v&1) ans=ans*u%p; u=u*u%p,v=v>>1;} return ans;
}
inline long long getans(int a,int b){
	return fac[a]*ifac[b]%p*ifac[a-b]%p;
}
int main(){
	cin>>n>>k,fac[0]=ifac[0]=1;
	for(int i=1;i<=n*k;i++) fac[i]=fac[i-1]*i%p,ifac[i]=pows(fac[i],p-2); dp[0][0]=1;
	for(int i=1;i<=n;i++)
		for(int j=0;j<=i;j++){
			if(j>0) dp[i][j]=(dp[i][j-1]*getans(n*k-(k-1)*(j-1)-i-1,k-2)+dp[i-1][j])%p;
			else dp[i][j]=dp[i-1][j];
		}
	if(k==1) cout<<1<<endl; else cout<<dp[n][n]*fac[n]%p<<endl;
    return 0;
}