[Solution] Maximal AND solution codeforces

[Solution] Maximal AND solution codeforces – Let $A N D$ denote the bitwise AND operation, and $O R$ denote the bitwise OR operation.

[Solution] Maximal AND solution codeforces

You are given an array $a$ of length $n$ and a non-negative integer $k$ . You can perform at most $k$ operations on the array of the following type:

Select an index $i$ ( $1 \leq i \leq n$ ) and replace $a_{i}$ with $a_{i}$ $O R$ $2^{j}$ where $j$ is any integer between $0$ and $30$ inclusive. In other words, in an operation you can choose an index $i$ ( $1 \leq i \leq n$ ) and set the $j$ -th bit of $a_{i}$ to $1$ ( $0 \leq j \leq 30$ ).

Output the maximum possible value of $a_{1}$ $A N D$ $a_{2}$ $A N D$ $\dots$ $A N D$ $a_{n}$ after performing at most $k$ operations.

Input

The first line of the input contains a single integer $t$ ( $1 \leq t \leq 100$ ) — the number of test cases. The description of test cases follows.

The first line of each test case contains the integers $n$ and $k$ ( $1 \leq n \leq 2 \cdot 10^{5}$ , $0 \leq k \leq 10^{9}$ ).

Then a single line follows, containing $n$ integers describing the arrays $a$ ( $0 \leq a_{i} < 2^{31}$ ).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^{5}$ .