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 maxn 2010
#define lim 5000010
#define mod 1000000007
using namespace std;
int fac[lim+10],inv[lim+10],dp[maxn][maxn],n,k;
int qpow(int a,int b){
	int ans=1,tmp=a;
	for(;b;b>>=1,tmp=1ll*tmp*tmp%mod)
		if(b&1)ans=1ll*ans*tmp%mod;
	return ans;
}
int C(int x,int y){
	return 1ll*fac[y]*inv[x]%mod*inv[y-x]%mod;
}
int cal(int pos,int x){
	return C(x-1,x+pos-1);
}
int main(){
	scanf("%d%d",&n,&k),inv[0]=fac[0]=1;
	if(k==1)return puts("1"),0;
	for(int i=1;i<lim;++i)fac[i]=1ll*fac[i-1]*i%mod;
	inv[lim-1]=qpow(fac[lim-1],mod-2);
	for(int i=lim-2;i>=1;--i)inv[i]=1ll*inv[i+1]*(i+1)%mod;
	dp[0][0]=1;
	for(int i=0;i<=n;++i)
		for(int j=i;j<=n;++j){
			dp[i+1][j]=(dp[i+1][j]+dp[i][j])%mod;
			dp[i][j+1]=(dp[i][j+1]+1ll*dp[i][j]*cal((j)*(k-1)+i,k-1))%mod;
		}
	printf("%d",1ll*dp[n][n]*fac[n]%mod);
}