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 NK = AB. 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.

Input

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

Output

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.

Sample

Input	Output
3 2 4 27 3 5 2	Case #1: 4 Case #2: 9 Case #3: 2