Odd-Even Subsequence
Description
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 $k$.
Input
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
Output a single integer — the minimum cost of a subsequence of size $k$.
Samples
4 2
1 2 3 4
1
4 3
1 2 3 4
2
5 3
5 3 4 2 6
2
6 4
5 3 50 2 4 5
3
Note
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 $min(max(3, 2), max(50, 4)) = 3$.