Description

Let $f_i$ denote the $i$-th element in the Fibonacci sequence, i.e. $f_1=f_2=1,f_n=f_{n-1}+f_{n-2}\ (n\ge 3)$. $x\mid y$ denotes $x$ divides $y$, i.e. $x$ is a divisor of $y$. For example, $3\mid 6, 1 \mid 1$ and $6 \mid 24$.

Then, let $S=\{s\mid s\in \mathbb{N}_+, f_n\mid f_s\}$. Given two integers $n$ and $k$, you need to find the $k$-th smallest element in the set $S$.

$\mathbb{N}_{+}$ denotes all positive integers, i.e. $\mathbb{N}_{+} = \{1,2,3,\ldots \}$.

Input

The first and only line of the input contains two integers $n,k$ $(1\le n,k \le 10^9)$.

Output

Output an integer, indicating the $k$-th smallest element in set $S$.

Samples

3 6

18

Note

Since $f_3=2$, $f_s$ can be $2, 8, 34, 144, 610, 2584, \ldots$, and $S=\lbrace3,6,9,12,15,18,\ldots\rbrace$, the sixth smallest element is $18$.

Resources

电子科技大学第十四届 ACM 趣味程序设计竞赛