You have an array of non-negative integers (a_1, a_2, \ldots, a_n). The value of a sub-array of length (\ge 2), (al, r = a_l, a_{l+1}, \ldots, a_r) is the minimum value of (a_i \oplus a_j) such that (l \le i < j \le r), where (\oplus) is the xor (exclusive-or) operator. You have to find the (k)-th smallest value over all sub-arrays of length (\ge 2). The first line of the input contains multiple test cases (t) ((1 \le t \le 2 \cdot 10^4)). The first line of each test case contains integer numbers (n) and (k) ((2 \le n \le 10^5), (1 \le k \le \frac{n\cdot(n-1)}{2})). The second line of the input contains (n) non-negative integer numbers (a_1, a_2, \ldots, a_n) ((0 \le a_i \le 10^9)) — the array itself. It is guaranteed that the sum of (n) over all test cases does not exceed (10^5). Print the (k)-th smallest value obtained over all subarrays of length at least (2). In the first testcase, we have subarrays with their smallest exclusive-or pair as: (1,2: 3) (2,3: 1) (3,4: 7) (4,5: 1) (1,2,3: 1) (2,3,4: 1) (3,4,5: 1) (1,2,3,4: 1) (2,3,4,5: 1) (1,2,3,4,5: 1) The sorted order would be: (1, 1, 1, 1, 1, 1, 1, 1, 3, 7). Therefore, the second smallest element would be (1).