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^YAX=BY.

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.

Constraints

Sample 1:

3
2 3
8 4
12 24

NO
YES
NO

Explanation:

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

Test case $2$: Let $X=2$ and $Y=3$. Thus, A^X = 8^2 = 64AX=82=64 and B^Y = 4^3 = 64BY=43=64. Thus, the pair $(8,4)$ is equivalent.

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