#P1114C. Trailing Loves (or L'oeufs?)
-
ID: 4613
Type: RemoteJudge
2000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Trailing Loves (or L'oeufs?)
No submission language available for this problem.
Description
Aki is fond of numbers, especially those with trailing zeros. For example, the number $9200$ has two trailing zeros. Aki thinks the more trailing zero digits a number has, the prettier it is.
However, Aki believes, that the number of trailing zeros of a number is not static, but depends on the base (radix) it is represented in. Thus, he considers a few scenarios with some numbers and bases. And now, since the numbers he used become quite bizarre, he asks you to help him to calculate the beauty of these numbers.
Given two integers $n$ and $b$ (in decimal notation), your task is to calculate the number of trailing zero digits in the $b$-ary (in the base/radix of $b$) representation of $n\,!$ (factorial of $n$).
The only line of the input contains two integers $n$ and $b$ ($1 \le n \le 10^{18}$, $2 \le b \le 10^{12}$).
Print an only integer — the number of trailing zero digits in the $b$-ary representation of $n!$
Input
The only line of the input contains two integers $n$ and $b$ ($1 \le n \le 10^{18}$, $2 \le b \le 10^{12}$).
Output
Print an only integer — the number of trailing zero digits in the $b$-ary representation of $n!$
Samples
6 9
1
38 11
3
5 2
3
5 10
1
Note
In the first example, $6!_{(10)} = 720_{(10)} = 880_{(9)}$.
In the third and fourth example, $5!_{(10)} = 120_{(10)} = 1111000_{(2)}$.
The representation of the number $x$ in the $b$-ary base is $d_1, d_2, \ldots, d_k$ if $x = d_1 b^{k - 1} + d_2 b^{k - 2} + \ldots + d_k b^0$, where $d_i$ are integers and $0 \le d_i \le b - 1$. For example, the number $720$ from the first example is represented as $880_{(9)}$ since $720 = 8 \cdot 9^2 + 8 \cdot 9 + 0 \cdot 1$.
You can read more about bases here.