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>
#include<algorithm>
#define fo(i,a,b) for(i=a;i<=b;i++)
#define fd(i,a,b) for(i=a;i>=b;i--)
using namespace std;
typedef long long ll;
const int maxn=2000+10,mo=1000000007;
int fac[maxn*maxn],inv[maxn*maxn];
int f[maxn][maxn];
int i,j,k,l,t,n,m,ans;
int qsm(int x,int y){
	if (!y) return 1;
	int t=qsm(x,y/2);
	t=(ll)t*t%mo;
	if (y%2) t=(ll)t*x%mo;
	return t;
}
int C(int n,int m){
	if (n<m||n<0) return 0;
	return (ll)fac[n]*inv[m]%mo*inv[n-m]%mo;
}
int main(){
	scanf("%d%d",&n,&k);
	if (k==1){
		printf("1\n");
		return 0;
	}
	fac[0]=1;
	fo(i,1,n*k) fac[i]=(ll)fac[i-1]*i%mo;
	inv[n*k]=qsm(fac[n*k],mo-2);
	fd(i,n*k-1,0) inv[i]=(ll)inv[i+1]*(i+1)%mo;
	f[0][0]=1;
	fo(i,0,n)
		fd(j,n,0)
			if (f[i][j]){
				if (j) (f[i][j-1]+=f[i][j])%=mo;
				if (i<n) (f[i+1][j+1]+=(ll)f[i][j]*C((i+1)*k-j-2,k-2)%mo)%=mo;
			}
	ans=(ll)f[n][0]*fac[n]%mo;
	(ans+=mo)%=mo;
	printf("%d\n",ans);
}