# [AGC002F] Leftmost Ball

## 输入输出格式

### 输入格式

The input is given from Standard Input in the following format:  $N$ $K$ 

### 输出格式

Print the number of the possible sequences of the colors of the balls after painting, modulo $10^9+7$ .

2 2

4

3 1

1

2 3

14

2000 2000

546381702

## 说明

### 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 - $1\ \leq\ N,K\ \leq\ 2,000$ ### Sample Explanation 1 The following $4$ sequences are possible: - $(0,1,0,2)$ - $(0,0,1,2)$ - $(0,2,0,1)$ - $(0,0,2,1)$ ### Sample Explanation 2 The following $1$ sequence is possible: - $(0,0,0)$