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Problem B
Pohlig-Hellman

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Implement the Pohlig-Hellman algorithm to solve $g^x \equiv h \pmod{p}$ for $x$.

Input

Input is three lines. The first line contains the prime $p$ where $3 \leq p < 2^{63}$ and each prime factor of $p-1$ are less than $2^{40}$. The second line contains the integer $g$ where $2 \leq g < p$ of order at least 2. The third line contains the integer $h$ where $0 \leq h < p$.

Output

Output one line with any valid solution $0 \leq x < p - 1$ or no solution if no solution exists.

Sample Input 1 Sample Output 1
3
2
1
0
Sample Input 2 Sample Output 2
449
6
99
182
Sample Input 3 Sample Output 3
7
4
3
no solution