Sequence-2

Vasili continues to create sequences. Today at school, he learned about the exponentiation operation, and decided to invent a new sequence.

First, he writes a natural number $A$ on the board. Each next number he writes will be equal to $A$ raised to the power of the previous number. In other words, the sequence is defined as follows:

Then, Vasili wants to find the element of this sequence with the smallest index that is divisible by a given number $N$. Since the numbers in the sequence can get very large, he needs your help.