LCC/Moose '19 Contest 4 J4 - Yes

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Points: 5 (partial)
Time limit: 1.0s
Memory limit: 64M

Problem types

Two numbers a and b are considered coprime if they do not have any common prime factors. For example, 4 and 9 are coprime, while 4 and 6 are not.

Given a and K, can you find the largest value of b such that a and b are coprime, and 1 < b \le K? You will be given T of these cases.

Input Specification

The first line will contain the integer T (T \in \{1,100\}), the number of cases. There will either be 1 case or 100 cases.

The next T lines will contain two integers, a, K (2 \le a, K \le 10^{16}). Note that these integers will not fit in a 32-bit data type (e.g. int). Please use a 64-bit data type (e.g. long).

Output Specification

For each case, output the value of b described in the problem statement on its own line. It is guaranteed the value exists.

Sample Input 1

14 28

Sample Output 1


Sample Input 2

30030 126

Sample Output 2



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