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 <cstdio>

const int mo=1000000007;
int dp[2005][2005],fac[4000005],inv[4000005];

int ksm(int x,int y){
	int i=1;
	for (;y;y>>=1,x=1ll*x*x%mo)
		if (y&1) i=1ll*i*x%mo;
	return i;
}

void calc(int n){
	fac[0]=1;
	for (int i=1;i<=n;i++) fac[i]=1ll*fac[i-1]*i%mo;
	inv[n]=ksm(fac[n],mo-2);
	for (int i=n;i>=1;i--) inv[i-1]=1ll*inv[i]*i%mo;
}

long long C(int n,int m){
	return 1ll*fac[n]*inv[m]%mo*inv[n-m]%mo;
}

int main(){
	int n,k;
	scanf("%d%d",&n,&k);
	if (k==1){
		puts("1");
		return 0;
	}
	calc(n*k);
	dp[0][0]=1;
	for (int i=0;i<=n;i++)
		for (int j=i;j<=n;j++){
			if (i) dp[i][j]=dp[i-1][j];
			if (j) dp[i][j]=(dp[i][j]+dp[i][j-1]*C(i+j*(k-1)-1,k-2))%mo;
		}
	printf("%lld\n",1ll*dp[n][n]*fac[n]%mo);
}