A13478. Odd-Even Subsequence

Ashish has an array $a$ of size $n$ .

A subsequence of $a$ is defined as a sequence that can be obtained from $a$ by deleting some elements (possibly none), without changing the order of the remaining elements.

Consider a subsequence $s$ of $a$ . He defines the cost of $s$ as the minimum between:

- The maximum among all elements at odd indices of $s$ .
- The maximum among all elements at even indices of $s$ .

Note that the index of an element is its index in $s$ , rather than its index in $a$ . The positions are numbered from $1$ . So, the cost of $s$ is equal to $min(max(s_1, s_3, s_5, \ldots), max(s_2, s_4, s_6, \ldots))$ .

For example, the cost of $\{7, 5, 6\}$ is $min( max(7, 6), max(5) ) = min(7, 5) = 5$ .

Help him find the minimum cost of a subsequence of size $k$ .

The first line contains two integers $n$ and $k$ ( $2 \leq k \leq n \leq 2 \cdot 10^5$ ) — the size of the array $a$ and the size of the subsequence.

The next line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 10^9$ ) — the elements of the array $a$ .

Output a single integer — the minimum cost of a subsequence of size $k$ .

In the first test, consider the subsequence $s$ = $\{1, 3\}$ . Here the cost is equal to $min(max(1), max(3)) = 1$ .

In the second test, consider the subsequence $s$ = $\{1, 2, 4\}$ . Here the cost is equal to $min(max(1, 4), max(2)) = 2$ .

In the fourth test, consider the subsequence $s$ = $\{3, 50, 2, 4\}$ . Here the cost is equal to $min(max(3, 2), max(50, 4)) = 3$ .