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;
typedef long long ll;
const int N=2005,mod=1e9+7;
int n,k,f[N][N],fac[N*N],ifac[N*N];
int Pow(int x,int k){
	int ret=1;
	while(k){
		if(k&1)ret=(ll)ret*x%mod;
		k>>=1;x=(ll)x*x%mod;
	}
	return ret;
}
int C(int n,int m){
	if(n<m)return 0;
	return (ll)fac[n]*ifac[n-m]%mod*ifac[m]%mod;
}
int main(){
	scanf("%d%d",&n,&k);
	fac[0]=1;
	for(int i=1;i<=n*k;i++)fac[i]=(ll)fac[i-1]*i%mod;
	for(int i=0;i<=n*k;i++)ifac[i]=Pow(fac[i],mod-2);
	if(k==1){
		puts("1");
		return 0;
	}
	f[0][0]=1;
	for(int i=0;i<n;i++)
		for(int j=i;j<=n;j++){
			f[i+1][j]=(f[i+1][j]+f[i][j])%mod;
			f[i][j+1]=(f[i][j+1]+(ll)f[i][j]*C((k-1)*j+i+k-2,k-2))%mod;
		}
	cout<<(ll)f[n][n]*fac[n]%mod<<"\n";
}