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C. Electrification

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAt 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

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

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.

Example

Input

3 3 2 1 2 5 2 1 1 1000000000 1 0 4

Output

3 500000000 4

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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