You are given an array $A$ containing $N$ integers. You can do the following operation at most $K$ times:

• Choose any index $i$ and increase the value of $A_i$ by $1$.

Your task is to find the maximum bitwise OR of the array.

Input format

• The first line contains an integer $T$ denoting the number of test cases.
• The first line of each test case contains two space-separated integers $N$ and $K$.
• The second line of each test case contains $N$ space-separated integers denoting array $A$.

Output format

For each test case, print the maximum possible bitwise OR of the array after performing at most $K$ operations in a new line.

Constraints

$1 \le T \le 100000\\ 1 \le N \le 200000\\ 0 \le K \le 1e18\\ 0 \le A_i \le 2^{60}$

It is guaranteed that the sum of $N$ over $T$ test cases does not exceed $1e6$.