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<cstring>
#include<algorithm>
#define N 2010
#define ll long long
#define mod 1000000007
using namespace std;
int n, m, jc[N*N], inv[N*N], f[N][N], ans;
int C(int n, int m){return (ll)jc[n]*inv[m]%mod*inv[n-m]%mod;}
int main(){
	scanf("%d%d", &n, &m);
	if(m==1){printf("1"); return 0;}
	jc[0]=1; for(int i=1; i<=4000000; i++)jc[i]=(ll)jc[i-1]*i%mod;
	inv[0]=inv[1]=1; for(int i=2; i<=4000000; i++)inv[i]=(ll)(mod-mod/i)*inv[mod%i]%mod;
	for(int i=1; i<=4000000; i++)inv[i]=(ll)inv[i]*inv[i-1]%mod;
	f[0][0]=1;
	for(int i=1; i<=n; i++)f[0][i]=(ll)f[0][i-1]*C(i*(m-1)-1, m-2)%mod;
	for(int i=1; i<=n; i++){
		f[i][i]=f[i-1][i];
		for(int j=i+1; j<=n; j++)f[i][j]=(f[i-1][j]+(ll)f[i][j-1]*C(i+j*(m-1)-1, m-2)%mod)%mod;
	}
	ans=(ll)f[n][n]*jc[n]%mod;
	printf("%d", ans);
	return 0;
}