Array Partition

Problem Description

Given $n$ integers, partition them into exactly $k$ subarrays. Find the maximum possible value of the bitwise AND of the sums of the subarrays.

Input Format

The first line contains two integers $n, k$.

Output Format

Output one line containing the maximum possible value of the bitwise AND of the sums.

Sample Input

3 2
1 2 3

Sample Output

3

Sample Explanation

There are only two cases:

1. $[1,2],[3]$: the answer is $(1+2)\ \&\ 3 = 3$.
2. $[1],[2,3]$: the answer is $1\ \&\ (2+3) = 1$.

Thus the answer is $3$.

Constraints

For $100\%$ of the data, $1 \le k \le n \le 100$ and $0 \le a_i \le 2^{50}$.