Leftmost Ball

题意翻译

给你n种颜色的球,每个球有k个,把这n*k个球排成一排,把每一种颜色的最左边出现的球涂成白色(初始球不包含白色),求有多少种不同的颜色序列,答案对1e9+7取模 翻译提供自[@asfasfasfad](https://www.luogu.org/space/show?uid=6300)

题目描述

[problemUrl]: https://agc002.contest.atcoder.jp/tasks/agc002_f

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 $ .

输入输出样例

输入样例 #1

2 2

输出样例 #1

4

输入样例 #2

3 1

输出样例 #2

1

输入样例 #3

2 3

输出样例 #3

14

输入样例 #4

2000 2000

输出样例 #4

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) $