Feluda likes strings and mathematics very much. As Feluda is still a child, he was only recently introduced to concept of powers. Being a novice guy, he thinks about powering strings as well as numbers. He defines A^n (A powered to n) to be A + A + ... + A which is a concatenation of n copies of A. For example "bhupkas"^2 = "bhupkasbhupkas".

He wants to check if given two strings A and B, can he find such positive integers n and m so that A ^ n = B ^ m. We are only interested in YES/NO answer, no need to give n and m values.

Input

First line contains integer T: number of test cases (T <= 100).

Single line per test case containing strings A and B. Both will be non-empty, of lengths of at most 10^5, composed only of lower case letters.

Output

For each test case, output "YES" if it possible to find integers n and m so that A ^ n = B ^ m or "NO" otherwise (quotes for clarity).

Example

Input:
3
a a
ab ba
praveen praveen
Output:
YES
NO
YES