We call a sequence of n non-negative integers A, awesome if there exists some positive integers x > 1 such that each element Ai in A (where 0 <= i < n) is evenly divisible by x. Recall that a evenly divides b if there exists some integers c such that b = a*c.

Given an awesome sequence, A and a positive integer k, find and print the maximum integer L, which satisfies the following conditions:

1. 0 <= L <= K
2. A U {L} is also awesome. (U is union operator)

Input:

The first line contains the integer t denoting the number of test cases. The next line contains two space-separated positive integers, n (length of the sequence A) and k (the upper bound of answer L).

The third line contains n space separated positive integers describing the elements of A.

Output:

For each test case, Print the value of L in a single line (where L is the maximum integer <= k and A U {L} is also awesome). As 0 is evenly divisible by any x > 1, there will always be an answer.   

Constraints:

1 <= t <= 12

1 <= n <= 100000

1 <= k <= 1000000000

1 <= Ai <= 1000000000