You will be given Q queries. In each query, you will be given two positive integers A and B. You have to find such positive integer K that there exist a positive integer N and N^K = A^B. If there exists multiple possible values for K, take the maximum of them.

For example, if A = 2 and B = 16 then K has to be 16.

First line of the input will contain a single integer Q. Then there will be Q lines. Each of the Q lines will contain two positive integers A and B.

1 ≤ Q ≤ 10⁶
2 ≤ A ≤ 10⁶
1 ≤ B ≤ 2*10⁹

For each test case print one line “Case #x: y” without quotations where x is the query number and y is the answer to the query described in the statement. See sample input-output for better understanding.