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 N 2005
#define ll long long
#define P 1000000007
using namespace std;
int n,k,inv[N*N],fac[N*N],ifac[N*N],dp[N][N];
int Get(int x,int y)
{
	return (ll)fac[x+y]*ifac[x]%P*ifac[y]%P;
}
int main()
{
	scanf("%d%d",&n,&k);
	if (k==1)
	{
		printf("%d\n",1);
		return 0;
	}
	inv[1]=fac[0]=fac[1]=ifac[0]=ifac[1]=1;
	for (int i=2;i<=n*k;i++)
	{
		inv[i]=(ll)(-P/i)*inv[P%i]%P;
		fac[i]=(ll)fac[i-1]*i%P;
		ifac[i]=(ll)ifac[i-1]*inv[i]%P;
	}
	dp[n+1][n+1]=1;
	for (int i=n+1;i>=1;i--)
	{
		for (int j=i;j>=1;j--)
		{
			if (i+j==n*2+2) continue;
			dp[i][j]=(dp[i+1][j]+(ll)dp[i][j+1]*Get((n-j)*(k-1)+n-i+1,k-2)%P)%P;
		}
	}
	printf("%lld\n",((ll)dp[1][1]*fac[n]%P+P)%P);
}