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 <cstdio>
#include <cstring>
int n,k,dp[2001][2001],fac[4000001],ifac[4000001];const int p=1e9+7;
inline int qpow(int bs,int ex){int ans=1;while(ex){if(ex&1)ans=1ll*ans*bs%p;bs=1ll*bs*bs%p;ex>>=1;}return ans;}
inline int binom(int n,int m){return 1ll*fac[n]*ifac[m]%p*ifac[n-m]%p;}
int main()
{
	scanf("%d%d",&n,&k);if(k==1){putchar(49);putchar(10);return 0;}
	fac[0]=1;for(int i=1;i<=n*k;++i)fac[i]=1ll*fac[i-1]*i%p;ifac[n*k]=qpow(fac[n*k],p-2);for(int i=n*k-1;~i;--i)ifac[i]=1ll*ifac[i+1]*(i+1)%p;
	for(int i=0;i<=n;++i)dp[i][0]=1;
	for(int i=1;i<=n;++i)
	{
		for(int j=1;j<=i;++j)
		{
			(dp[i][j]+=dp[i-1][j])%=p;
			(dp[i][j]+=1ll*dp[i][j-1]*(n-j+1)%p*binom(n*k-i-1-(j-1)*(k-1),k-2)%p)%=p;
		}
	}
	printf("%d\n",dp[n][n]);return 0;
}