Description:
At first, there was a legend related to the name of the problem, but now it's just a formal statement.
You are given $$$n$$$ points $$$a_1, a_2, \dots, a_n$$$ on the $$$OX$$$ axis. Now you are asked to find such an integer point $$$x$$$ on $$$OX$$$ axis that $$$f_k(x)$$$ is minimal possible.
The function $$$f_k(x)$$$ can be described in the following way:
- form a list of distances $$$d_1, d_2, \dots, d_n$$$ where $$$d_i = |a_i - x|$$$ (distance between $$$a_i$$$ and $$$x$$$);
- sort list $$$d$$$ in non-descending order;
- take $$$d_{k + 1}$$$ as a result.
If there are multiple optimal answers you can print any of them.
Input Format:
The first line contains single integer $$$T$$$ ($$$ 1 \le T \le 2 \cdot 10^5$$$) — number of queries. Next $$$2 \cdot T$$$ lines contain descriptions of queries. All queries are independent.
The first line of each query contains two integers $$$n$$$, $$$k$$$ ($$$1 \le n \le 2 \cdot 10^5$$$, $$$0 \le k < n$$$) — the number of points and constant $$$k$$$.
The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_1 < a_2 < \dots < a_n \le 10^9$$$) — points in ascending order.
It's guaranteed that $$$\sum{n}$$$ doesn't exceed $$$2 \cdot 10^5$$$.
Output Format:
Print $$$T$$$ integers — corresponding points $$$x$$$ which have minimal possible value of $$$f_k(x)$$$. If there are multiple answers you can print any of them.
Note:
None