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D. Odd-Even Subsequence

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAshish 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 $$$k$$$.

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 $$$k$$$.

Examples

Input

4 2 1 2 3 4

Output

1

Input

4 3 1 2 3 4

Output

2

Input

5 3 5 3 4 2 6

Output

2

Input

6 4 5 3 50 2 4 5

Output

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 $$$min(max(3, 2), max(50, 4)) = 3$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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