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 <algorithm>
const long long MOD = 1000000007;
int N, K;
long long O, fc[4000001], fi[4000001], f[2001], g[2001];
inline long long C(int x, int y)
{
	return fc[x] * fi[y] % MOD * fi[x - y] % MOD;
}
int main()
{
	scanf("%d%d", &N, &K);
	if (K == 1)
	{
		puts("1");
		return 0;
	}
	fc[0] = fi[0] = fi[1] = 1;
	for (int i = 2; i <= N * K; i++)
		fi[i] = (MOD - MOD / i) * fi[MOD % i] % MOD;
	for (int i = 1; i <= N * K; i++)
	{
		fc[i] = fc[i - 1] * i % MOD;
		fi[i] = fi[i - 1] * fi[i] % MOD;
	}
	f[0] = 1;
	for (int i = 1; i <= N + N; i++)
	{
		for (int j = 0; j < (i + 1) >> 1; j++)
			g[j] = 0;
		for (int j = (i + 1) >> 1; j <= N; j++)
			g[j] = (f[j - 1] * C(i + j * (K - 2) - 1, K - 2) + f[j]) % MOD;
		std::copy(g, g + N + 1, f);
	}
	printf("%lld\n", f[N] * fc[N] % MOD);
	return 0;
}