Problem Statement

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 $10^9+7$.