Counting is very difficult so Veshy asks you for help. You are given two positive integers, $a$ and $b$. You want to find the highest power of $a$, $n$, that will divide into $b!$. In other words, you want to find the maximum $n$ such that $a^n$ divides into $b!$.

Input Specification

The input is a single line containing two space-separated integers, $a$ and $b$ in that order. $2\le a<b\le {10}^6$

Output Specification

Output on a single line, the number $n$ such that $a^n$ divides into $b!$ and $n$ is the greatest possible.

Sample Input 1

8 849

Sample Output 1

281

Sample Input 2

2 2020

Sample Output 2

2013

Explanation

In sample input 1, $8^{281}$ is the highest power of $8$ that can divide into $849!$.
In sample input 2, $2^{2013}$ is the highest power of $2$ that can divide into $2020!$.