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Problem J
Factovisors
The factorial function, $n!$ is defined thus for $n$ a non-negative integer:
\[ n! = \begin{cases} 1 & \text {if $n = 0$} \\ n \cdot (n-1)! & \text {if $n > 0$} \end{cases} \]We say that $a$ divides $b$ if there exists an integer $k$ such that $k \cdot a = b$.
Input
The input to your program consists of several lines, each containing two non-negative integers, $n$ and $m$, both less than $2^{31}$.
Output
For each input line, output a line stating whether or not $m$ divides $n!$, in the format shown below.
| Sample Input 1 | Sample Output 1 |
|---|---|
6 9 6 27 20 10000 20 100000 1000 1009 |
9 divides 6! 27 does not divide 6! 10000 divides 20! 100000 does not divide 20! 1009 does not divide 1000! |