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>

using namespace std;

const int N=2010,Mod=1e9+7;

int n,k,fact[N*N],inv[N*N],f[2*N][N];

void Init() { scanf("%d%d",&n,&k); }

void Prepare()
{
	fact[0]=1; for (int i=1;i<=n*k;++i) fact[i]=1ll*fact[i-1]*i%Mod;
	inv[0]=inv[1]=1; for (int i=2;i<=n*k;++i) inv[i]=1ll*(Mod-Mod/i)*inv[Mod%i]%Mod;
	for (int i=1;i<=n*k;++i) inv[i]=1ll*inv[i-1]*inv[i]%Mod;
}

int Calc(int n,int m) { if (n<0 || n<m) return 0; return 1ll*fact[n]*inv[n-m]%Mod*inv[m]%Mod; }

void Solve()
{
	if (k==1) { printf("1\n"); return ; }
	Prepare();
	f[0][0]=1;
	for (int i=0;i<2*n;++i)
		for (int j=0;j<=i && j<=n;++j)
			if (f[i][j])
			{
				if (j<n) f[i+1][j+1]=(f[i+1][j+1]+f[i][j])%Mod;
				if (j>0) f[i+1][j-1]=(f[i+1][j-1]+1ll*f[i][j]%Mod*Calc(n*k-(i-j)/2*k-j-1,k-2)%Mod)%Mod;
			}
	printf("%lld\n",1ll*f[2*n][0]*fact[n]%Mod);
}

int main()
{
	Init();
	Solve();
	return 0;
}