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>
#define int long long
#define N 4000005
#define MOD 1000000007
using namespace std;
int n,k,f[2005][2005],inv[N],fac[N],infac[N];
int C(int x,int y){
	return x>=y ? fac[x]*infac[y]%MOD*infac[x-y]%MOD : 0;
}
signed main(){
	cin>>n>>k;
	if(k==1){
		cout<<1<<endl;
		return 0;
	}
	fac[0]=infac[0]=inv[1]=1;//first deal
	for(int i=1;i<=n*k;i++)
		fac[i]=fac[i-1]*i%MOD;
	for(int i=2;i<=n*k;i++)
		inv[i]=inv[MOD%i]*(MOD-MOD/i)%MOD;
	for(int i=1;i<=n*k;i++)
		infac[i]=infac[i-1]%MOD*inv[i]%MOD;
	for(int i=1;i<=n;i++)
		f[i][0]=1;
	for(int i=1;i<=n;i++){
		for(int j=1;j<=i;j++){
//			cout<<i<<" "<<j<<"*"<<"%"<<C(k-2,(n-i)+(n-j+1)*(k-1)-1)<<endl;
			f[i][j]=(f[i-1][j]+C((n-i)+(n-j+1)*(k-1)-1,k-2)*f[i][j-1]%MOD*(n-j+1)%MOD)%MOD;
//			cout<<f[1][1]<<endl;
		}
	}
	cout<<f[n][n];
	return 0;
}