Besides the ordinary Boy Friend and Girl Friend, here we define a more academic kind of friend: Prime Friend. We call a nonnegative integer A is the integer B’s Prime Friend when the sum of A and B is a prime.
So an integer has many prime friends, for example, 1 has infinite prime friends: 1, 2, 4, 6, 10 and so on. This problem is very simple, given two integers A and B, find the minimum common prime friend which will make them not only become primes but also prime neighbor. We say C and D is prime neighbor only when both of them are primes and integer(s) between them is/are not.
The first line contains a single integer T, indicating the number of test cases.
Each test case only contains two integers A and B.
Technical Specification
1. 1 <= T <= 1000
2. 1 <= A, B <= 150
For each test case, output the case number first, then the minimum common prime friend of A and B, if not such number exists, output -1.