k-置换 - Problème

#12871. k-置换

Statistiques

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

给定一个包含 $n$ 个元素的恒等排列，你需要求出通过不超过 $k$ 次对换（transposition）可以得到的排列数量。由于结果可能非常大，请输出其对 $10^9 + 7$ 取模的结果。

对换是指交换排列中两个不同位置的元素的操作。

输入格式

输入仅一行，包含两个用空格隔开的整数 $n$ 和 $k$ ($1 \le n \le 10^9, 0 \le k \le 3000$)。

输出格式

输出一个整数，即问题的答案对 $10^9 + 7$ 取模的结果。

样例

样例输入 1

4 1

样例输出 1

样例输入 2

4 2

样例输出 2

样例输入 3

7 7

样例输出 3

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