K-th Largest n-Pseudo Smooth Number

An integer \(m > 1\) is defined to be an n-pseudo smooth number if the following condition holds. Let the (not necessarily distinct) prime factorization of \(m\) have \(k\) factors \(a_1, a_2, \dots, a_k\) with \(a_1 \le a_2 \le \cdots \le a_k\). If the largest prime factor \(a_k\) satisfies

[ a_k^{k}\le n, \quad \text{and} \quad a_k \le 397, ]

then \(m\) is called an n-pseudo smooth number.

Given two integers \(n\) and \(k\), find the k-th largest n-pseudo smooth number. It is guaranteed that the answer exists.

inputFormat

The input consists of a single line containing two space-separated integers \(n\) and \(k\).

\(n\) is used in the condition \(a_k^{k} \le n\) and \(k\) denotes that you have to output the k-th largest n-pseudo smooth number.

outputFormat

Output a single integer, the k-th largest n-pseudo smooth number.

sample

10 1

8