Best Subsequence

You are given an array $w_1, w_2, \ldots, w_n$ of length $n$.

You need to choose a subsequence of $k$ elements. Let their indices be $1 \le i_1 < i_2 < \ldots < i_k \le n$.

Your goal is to find the minimum possible value of

$\max(w_{i_1} + w_{i_2}, w_{i_2} + w_{i_3}, \ldots, w_{i_{k-1}} + w_{i_k}, w_{i_k} + w_{i_1})$

among all such subsequences.

The first line contains two integers $n$ and $k$ ($3 \le k \le n \le 200000$), the length of the array and the length of the subsequence.

The second line contains $n$ space-separated integers $w_1, w_2, \ldots, w_n$ ($1 \le w_i \le 10^9$).

Print one integer: the minimum possible value of the expression above over all subsequences of length $k$.