[Solution] Equivalent Numbers CodeChef Solution

Problem

Chef calls a pair of integers $(A, B)$ equivalent if there exist some positive integers $X$ and $Y$ such that $A^X = B^Y$.

Given $A$ and $B$, determine whether the pair is equivalent or not.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• Each test case consists of two space-separated integers $A$ and $B$, as mentioned in statement.

Output Format

For each test case, output YES if $(A, B)$ is an equivalent pair, NO otherwise.

The output is case-insensitive. Thus, the strings Yes, YES, yes, and yeS are all considered identical.

Explanation:

Test case $1$: There are no positive integers $X$ and $Y$ which satisfy $A^X = B^Y$.

Test case $2$: Let $X = 2$ and $Y = 3$. Thus, $A^X = 8^2 = 64$ and $B^Y = 4^3 = 64$. Thus, the pair $(8, 4)$ is equivalent.

Test case $3$: There are no positive integers $X$ and $Y$ which satisfy $A^X = B^Y$.