道路规划 - Problem

#843. 道路规划

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The problem was used in the following contests:

Elegia's Forgotten Hill

This problem is prepared by Elegia .

R 国的人们生活在一个有 $k$ 条街道的城市里，每条街道上坐落着 $n$ 栋房子，它们有秩序地按方阵排布。起初每两个街对面的房子也都是有道路联通的。简要说就是这些房子是以网格状道路联通的。然而最近市政府资金紧张，难以维护如此多的道路，因此不得不尽量减少道路的数量，但又要保证任意两栋房子都有道路能联通。注意，这里街上的道路也是可以拆掉一部分的。不难看出最后只会剩下 $kn - 1$ 条道路。请你计算一下，一共有多少种方案能满足这一要求？

答案对 $P = 10^9 + 7$ 取模。

输入格式

一行两个整数 $k, n$。

输出格式

输出一个数，表示答案。

样例数据

样例 1 输入

2 2

样例 1 输出

子任务

测试点编号	$k \le $	$n \le $
$1$	$2$	$5$
$2$	$3$	$5$
$3$	$2$	$10^5$
$4$	$2$	$10^9$
$5$	$3$	$10^4$
$6$	$4$
$7$	$5$
$8$	$5$	$10^9$
$9$	$6$	$10^3$
$10$	$6$	$10^9$

对于 $100\%$ 的数据，保证 $2 \le k \le 6$, $1 \le n \le 10^9$

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