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>
using namespace std;
typedef long long ll;
#define mod 1000000007
int n,k;
ll dp[2005][2005];
ll modpow(ll x,ll n){
	ll res=1;
	while(n>0){
		if(n&1) res=res*x%mod;
		x=x*x%mod;
		n>>=1;
	}
	return res;
}
ll F[4000005],R[4000005];
void make(){
	F[0] = 1;
	for(int i=1;i<4000005;i++) F[i] = F[i-1]*i%mod;
	R[4000000] = modpow(F[4000000],mod-2);
	for(int i=4000000;i>=1;i--) R[i-1] = R[i]*1LL*i%mod;
}
ll C(int a,int b){
	return F[a]*R[b]%mod*R[a-b]%mod;
}
int main(){
	cin>>n>>k; if(k==1){puts("1");return 0;} make();
	dp[0][0] = 1;
	for(int i=0;i<=n;i++){
		for(int j=0;j<=n;j++){
			if(dp[i][j] == 0) continue;
			if(i!=n) dp[i+1][j] = (dp[i+1][j]+dp[i][j])%mod;
			if(i>=j+1) dp[i][j+1] = (dp[i][j+1]+dp[i][j]*C(n*k-j*(k-1)-i-1,k-2)%mod)%mod;
		}
	}
	cout<<dp[n][n]*F[n]%mod<<endl;
}