Zenyk recently got an array with his $n$ school grades $a_1, a_2, ..., a_n$. He isn't very happy with them and knows that his parents also will not be happy with his grades. But he also knows that his parents evaluate his performance in a very strange way. They care only about the middle element in the array of grades Zenyk got. More formally if Zenyk's array is $b$ and it has $m$ elements, $b_{\left\lfloor{(m+1)/2}\right\rfloor}$ is Zenyk's performance. Zenyk doesn't want to disappoint his parents, so he wants to erase exactly $k (k < n)$ grades from his array $a$ in order to maximize his score.

Input format

The first line contains two integers $n, k (1 \le k < n \le 10^{5})$ --- the number of Zenyk's grades and the number of grades Zenyk should delete, respectively.
The second line contains $n$ integers $a_1, a_2, ..., a_n$ ($1 \le a_i \le 10^{9}$) --- Zenyk's grades.

Output format

You should output only one integer --- maximum score Zenyk can get.