K. And X Elements
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array $$$a$$$ of $$$n$$$ elements and an integer $$$x$$$. You also have a variable $$$v$$$ which is initially equal to $$$0$$$.

You will perform exactly one operation for each element of the array, and the operations must be applied in the order of the array (i.e., from $$$a_1$$$ to $$$a_n$$$). For each $$$i$$$ from $$$1$$$ to $$$n$$$, you can choose one of the following operations:

  1. $$$v = v \mid a_i$$$ (bitwise OR)
  2. $$$v = v \space \& \space a_i$$$ (bitwise AND)

You must use the second operation (AND) at least $$$x$$$ times throughout the process.

Determine the maximum possible value of $$$v$$$ at the end.

Input

The first line of input contains one integer $$$t$$$ $$$(1$$$ $$$\le$$$ $$$t$$$ $$$\le$$$ $$$1000)$$$, the number of test cases.

The first line of each test case contains two integers $$$n$$$ and $$$x$$$ $$$(1$$$ $$$\le$$$ $$$x$$$ $$$\le$$$ $$$n$$$ $$$\le$$$ $$$10^5)$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1,a_2,..,a_n$$$ $$$(0 \le a_i \le 10^5)$$$, the elements of the array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, print in a separate line the maximum value possible for $$$v$$$ after the $$$n$$$ operations.

Example
Input
3
2 1
2 2
3 2
0 3 2
4 1
1 0 2 3
Output
2
2
3