CF1370D 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 $ .