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!~.