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;
#define mod 1000000007
#define MX 4000000
int dp[2005][2005];
long long fact[MX+5],inv[MX+5];
long long pow_log(long long x,int y)
{
	if (!y)
	return 1;
	long long ret=pow_log(x,y/2);
	ret=(ret*ret)%mod;
	if (y%2)
	ret=(ret*x)%mod;
	return ret;
}
long long ncr(int n,int r)
{
	return ((fact[n]*inv[r])%mod*inv[n-r])%mod;
}
int n,k;
int solve(int w,int c)
{
	if (w==n && c==n)
	return 1;
	if (dp[w][c]!=-1)
	return dp[w][c];
	int ret=0;
	if (w!=n)
	ret=solve(w+1,c);
	if (c<w)
	ret=(ret+solve(w,c+1)*ncr(n*k-w-c*(k-1)-1,k-2)%mod*(n-c))%mod;
	return dp[w][c]=ret;
}
int main()
{
	fact[0]=1;
	for (int i=1;i<=MX;i++)
	fact[i]=(i*fact[i-1])%mod;
	inv[MX]=pow_log(fact[MX],mod-2);
	for (int i=MX-1;i>=0;i--)
	inv[i]=((i+1)*inv[i+1])%mod;
	scanf("%d%d",&n,&k);
	if (k==1)
	{
		printf("1");
		return 0;
	}
	memset(dp,-1,sizeof(dp));
	printf("%d",solve(0,0));
}