Given integers $a,n,p$, find the smallest nonnegative integer $x$ such that $a^x\equiv n(\mathrm{mod}p)$.

Constraints

$1<a,n,p<2^{31}$

$p$ is a prime number.

Input Specification

The only line contains three space-separated integers, $a$, $n$, and $p$.

Output Specification

Output the smallest possible nonnegative integer $x$; if no such $x$ exists, output DNE.

Sample Input 1

7 4 5

Sample Output 1

2

Sample Input 2

10 7 11

Sample Output 2

DNE