You are given an array \(A\) having \(N\) integers and an integer \(X\). Find the length of the longest non-empty subsequence of the array \(A\) such that the Bitwise AND of the elements of the subsequence is greater than or equal to \(X\). Print \(-1\) if no such subsequence exists.

A subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements.

Input format

The first line of input contains an integer \(T\) denoting the number of test cases. The description of each test case is as follows:
The first line of each test case contains two integers \(N\) and \(X\).
The second line of each test case contains \(N\) integers \(A_1, A_2,\dots, A_N\).

Output format

For each test case, print \(-1\) if no subsequence satisfies the given condition. Otherwise, print the length of the longest non-empty subsequence in a separate line.

Constraints

\(1\le T \le 10^4 \\ 1 \leq N \le 10^5\\ 1\le A_i , X\lt 2^{30}\\ \text{Sum of $N$ over all test cases does not exceed }3\cdot 10^5.\)