The beauty of an array $$$b$$$ of length $$$m$$$ is defined as $$$\max(b_i \oplus b_j)$$$ among all possible pairs $$$1 \le i \le j \le m$$$, where $$$x \oplus y$$$ is the bitwise XOR of numbers $$$x$$$ and $$$y$$$. We denote the beauty value of the array $$$b$$$ as $$$f(b)$$$.

An array $$$b$$$ is called beautiful if $$$f(b) \ge k$$$.

Recently, Kostya bought an array $$$a$$$ of length $$$n$$$ from the store. He considers this array too long, so he plans to cut out some beautiful subarray from it. That is, he wants to choose numbers $$$l$$$ and $$$r$$$ ($$$1 \le l \le r \le n$$$) such that the array $$$a_{l \dots r}$$$ is beautiful. The length of such a subarray will be the number $$$r - l + 1$$$. The entire array $$$a$$$ is also considered a subarray (with $$$l = 1$$$ and $$$r = n$$$).

Your task is to find the length of the shortest beautiful subarray in the array $$$a$$$. If no subarray is beautiful, you should output the number $$$-1$$$.

Input

The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$).

Next, there are $$$t$$$ blocks of two lines:

In the first line of the block, there are two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 2 \cdot 10^5$$$, $$$0 \le k \le 10^9$$$).

In the second line of the block, there is the array $$$a$$$ consisting of $$$n$$$ integers ($$$0 \le a_i \le 10^9$$$).

It is guaranteed that the sum of $$$n$$$ across all tests does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, you need to output a single integer — the minimum length of the segment $$$(l, r)$$$ for which $$$f(a_{l \dots r}) \ge k$$$. If such a segment is not found, you should output $$$-1$$$.

Shorten the Array

Examples