B"Let mathsf{AND} denote the bitwise AND operation, and mathsf{OR} denote the bitwise OR operation. You are given an array a of length n and a non-negative integer k . You can perform at most k operations on the array of the following type: Output the maximum possible value of a_1 mathsf{AND} a_2 mathsf{AND} ... mathsf{AND} a_n after performing at most k operations. The first line of the input contains a single integer t ( 1 <= t <= 100 ) -- the number of test cases. The description of test cases follows. The first line of each test case contains the integers n and k ( 1 <= n <= 2 cdot 10^5 , 0 <= k <= 10^9 ). Then a single line follows, containing n integers describing the arrays a ( 0 <= q a_i < 2^{31} ). It is guaranteed that the sum of n over all test cases does not exceed 2 cdot 10^5 . For each test case, output a single line containing the maximum possible mathsf{AND} value of a_1 mathsf{AND} a_2 mathsf{AND} ... mathsf{AND} a_n after performing at most k operations. For the first test case, we can set the bit 1 ( 2^1 ) of the last 2 elements using the 2 operations, thus obtaining the array [ 2 , 3 , 3 ], which has mathsf{AND} value equal to 2 . For the second test case, we can't perform any operations so the answer is just the mathsf{AND} of the whole array which is 4 . "...