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 $$1e6$$.