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Problem F
Factorial Power
Given integers $n$ and $m$, determine the largest $k$ for which $n^ k$ divides $m! = 1 \cdot 2 \cdots (m - 1) \cdot m$.
Input
The first and only line of input contains the integers $n$ and $m$ ($2 \le n, m \le 10^{14}$).
Output
Output the integer $k$ from the task description.
| Sample Input 1 | Sample Output 1 |
|---|---|
6 3 |
1 |
| Sample Input 2 | Sample Output 2 |
|---|---|
123 123123123 |
3078076 |
