Score : $300$ points
Given is an integer $N$. Determine whether there is a pair of positive integers $(A, B)$ such that $3^A + 5^B = N$, and find one such pair if it exists.
Input is given from Standard Input in the following format:
If there is no pair $(A, B)$ that satisfies the condition, print
If there is such a pair, print $A$ and $B$ of one such pair with space in between. If there are multiple such pairs, any of them will be accepted.
We have $3^4 + 5^2 = 81 + 25 = 106$, so $(A, B) = (4, 2)$ satisfies the condition.