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>
#define ll long long
const int N=2005,M=4e6+5,mo=1e9+7;
int n,m,nm,i,j,f[N];
int fact[M],inv[M],fv[M];
void init(int n){
	fact[0]=fact[1]=inv[1]=fv[0]=fv[1]=1;
	for (i=2;i<=n;i++){
		fact[i]=(ll)fact[i-1]*i%mo;
		inv[i]=(ll)inv[mo%i]*(mo-mo/i)%mo;
		fv[i]=(ll)fv[i-1]*inv[i]%mo;
	}
}
int C(int n,int m){return (ll)fact[n]*fv[m]%mo*fv[n-m]%mo;}
int main(){
	scanf("%d%d",&n,&m);m--;
	if (!m){puts("1");return 0;}
	nm=n*m+n;init(nm);f[0]=1;
	for (i=1;i<=n;i++) for (j=1;j<=i;j++)
		f[j]=(f[j]+(ll)(n-j+1)*
			C(nm-i-(j-1)*m-1,m-1)%mo*f[j-1])%mo;
	printf("%d",f[n]);
}