伪光滑数 - Problem

#15783. 伪光滑数

Statistics

若一个大于 $1$ 的整数 $M$ 的质因数分解有 $k$ 项，其最大的质因子为 $a_k$，并且满足 ${a_k}^k \leq N$，$a_k < 128$，我们就称整数 $M$ 为 $N$-伪光滑数。

现在给出 $N$，求所有整数中，第 $K$ 大的 $N$-伪光滑数。

输入格式

只有一行，为用空格隔开的整数 $N$ 和 $K$。

输出格式

只有一行，为一个整数，表示答案。

样例数据

样例 1 输入

12345 20

样例 1 输出

子任务

对于 $30\%$ 的数据，$N \leq 10^6$；

对于 $100\%$ 的数据，$2 \leq N \leq 10^{18}$，$1 \leq K \leq 800000$。保证至少有 $K$ 个满足要求的数。

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