素数素数幂 - 問題

#12299. 素数素数幂

統計

この問題は以下のコンテストで使用されています：

Potyczki Algorytmiczne 2011, Finał

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

在本题中，我们只关注素数幂，即形如 $a^{b}$ 的数，其中 $a$ 和 $b$ 均为素数。对于给定的数 $n$，我们希望找到大于 $n$ 的第 $k$ 小的素数幂。

输入格式

输入的第一行也是唯一一行包含两个整数 $n$ 和 $k$ ($1 \le n \le 10^{18}$，$1 \le k \le 100\,000$)。

输出格式

输出的第一行也是唯一一行应包含一个整数 $m$，使得 $m$ 是大于 $n$ 的第 $k$ 小的素数幂。

样例

输入 1

22 1

输出 1

输入 2

22 2

输出 2

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