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;
const int MAXN=2005,MOD=1e9+7;
int n,k,fac[MAXN*MAXN],inv[MAXN*MAXN],dp[MAXN][MAXN];

ll quick_pow(ll a,ll b)
{
	ll ret=1;
	for(;b;b>>=1,a=a*a%MOD)
		if(b&1) ret=ret*a%MOD;
	return ret;
}
ll C(int a,int b)
{if(a<b) return 0;return 1ll*fac[a]*inv[a-b]%MOD*inv[b]%MOD;}

int main()
{
	scanf("%d%d",&n,&k);
	if(k==1) return puts("1"),0;
	fac[0]=dp[0][0]=1;
	for(int i=1;i<=n*k;i++) fac[i]=1ll*fac[i-1]*i%MOD;
	inv[n*k]=quick_pow(fac[n*k],MOD-2);
	for(int i=n*k-1;i>=0;i--) inv[i]=1ll*inv[i+1]*(i+1)%MOD;
	
	for(int i=0;i<=n;i++)
		for(int j=1;j<=n;j++)
			if(j<=i) dp[i][j]=dp[i-1][j];
			else dp[i][j]=(dp[i][j-1]*C(i+(k-1)*j-1,k-2)%MOD+dp[max(0,i-1)][j])%MOD;
	
	ll res=1ll*dp[n][n]*fac[n]%MOD;
	printf("%lld",res);
	return 0;
}