Maximum Bitwise AND of K Elements

Given an array of n integers and an integer k, your task is to choose exactly k elements from the array such that the bitwise AND of these elements is maximized.

The bitwise AND operation for a set of numbers \(a_1, a_2, \dots, a_k\) is defined as:

[ a_1 ;&; a_2 ;&; \dots ;&; a_k ]

You should read the input from stdin and print the result to stdout. It is guaranteed that the size of the input will be small enough to allow a brute-force solution.

inputFormat

The input is given in two lines:

• The first line contains two integers, \(n\) and \(k\), where \(n\) is the number of elements in the array and \(k\) is the number of elements to select.
• The second line contains \(n\) space-separated integers representing the array.

outputFormat

Output a single integer to stdout representing the maximum bitwise AND value obtained by choosing exactly \(k\) elements from the array.

## sample

5 3
6 4 7 8 1

4

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