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 ll long long
#define mod 1000000007
#define N 2009
#define M 4000009
#define cbn(x,y) ((ll)fac[x]*inv[y]%mod*inv[(x)-(y)]%mod)
using namespace std;

int n,m,tot,fac[M],inv[M],dp[N][N];
int main(){
	scanf("%d%d",&n,&m); tot=n*m;
	if (m==1){ puts("1"); return 0; }
	int i,j;
	fac[0]=inv[0]=inv[1]=1;
	for (i=1; i<=tot; i++) fac[i]=(ll)fac[i-1]*i%mod;
	for (i=2; i<=tot; i++) inv[i]=mod-(ll)inv[mod%i]*(mod/i)%mod;
	for (i=2; i<=tot; i++) inv[i]=(ll)inv[i-1]*inv[i]%mod;
	dp[1][0]=fac[n];
	for (i=1; i<=n; i++)
		for (j=0; j<=i; j++){
			if (i<n) dp[i+1][j]=(dp[i+1][j]+dp[i][j])%mod;
			if (j<i) dp[i][j+1]=(dp[i][j+1]+(ll)dp[i][j]*cbn(tot-i-(m-1)*j-1,m-2))%mod;

		}
	printf("%d\n",dp[n][n]); 
	return 0;
}