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 
using namespace std;
const int N=2200;
const int MAXN=4e6;
const int M=1e9+7;
ll fac[N*N],inv[N*N],f[N][N];
int n,k;
inline ll qpow(ll a,ll b){
	ll ans=1;
	while(b){
		if(b&1) ans=ans*a%M;
		b>>=1;a=a*a%M;
	} 
	return ans;
}
void init(){
	fac[0]=1;
	for(int i=1;i<=MAXN;i++) fac[i]=fac[i-1]*i%M;
	inv[MAXN]=qpow(fac[MAXN],M-2); 
	for(int i=MAXN;i>=1;i--) inv[i-1]=inv[i]*i%M;
}
inline ll C(int n,int m){
	if(n<m) return 0;
	return fac[n]*inv[m]%M*inv[n-m]%M;
}
int main(){
//	freopen("at2000.in","r",stdin);
	init();
	scanf("%d%d",&n,&k);f[0][0]=1;
	if(k==1) {printf("1\n");return 0; } 
	for(int i=1;i<=n;i++)
		for(int j=0;j<=i;j++) f[i][j]=(f[i-1][j]+(n-j+1)*C(n*k-i-(j-1)*(k-1)-1,k-2)%M*f[i][j-1])%M;
	printf("%lld\n",f[n][n]);
	return 0;
}