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Problem A
Shanks' Baby Step Giant Step
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Implement the baby-step giant-step algorithm to solve $g^x \equiv h \pmod{p}$ for $x$.
Input
Input is three lines. The first line contains the prime $p$ where $3 \leq p < 2^{40}$. 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 |
|---|---|
367 2 137 |
75 |
| Sample Input 2 | Sample Output 2 |
|---|---|
367 2 179 |
no solution |
