Mr. Knife has drafted $$$n$$$ absurd posts for a channel on a chat platform. His goal is to farm pill emoji reactions. Unfortunately, the channel's pill-farming bot uses an unnecessarily elaborate scoring rule.
The drafts have absurdity ratings $$$a_1, a_2, \ldots, a_n$$$, which may be negative. Mr. Knife must publish exactly $$$m$$$ drafts in their original order. Their ratings form a subsequence$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ with length $$$m$$$.
His pill score starts at $$$0$$$. When he publishes the $$$i$$$-th chosen draft, the bot changes his score by $$$i \cdot (b_i - b_{i-1})$$$, where $$$b_0 = 0$$$. A negative change deducts points, and the score is allowed to become negative. Thus, his final pill score is $$$$$$ \sum_{i = 1}^{m} i \cdot (b_i - b_{i - 1}). $$$$$$
What is the maximum pill score Mr. Knife can obtain by choosing which drafts to publish?
$$$^{\text{∗}}$$$A sequence $$$a$$$ is a subsequence of a sequence $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by the deletion of several (possibly, zero or all) elements from arbitrary positions.
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.
The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le m \le n \le 2 \cdot 10^5$$$) — the number of drafts and the number of posts Mr. Knife must publish.
The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-10^7 \le a_i \le 10^7$$$) — the absurdity ratings of the drafts.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
For each test case, print one integer — the maximum pill score Mr. Knife can obtain by publishing exactly $$$m$$$ drafts in their original order.
65 30 8 1 7 34 30 -4 10 -24 20 5 -2 46 30 9 8 7 6 51 173 25 -100 4
203410157108
In the first test case, Mr. Knife can publish the drafts with ratings $$$[0, 1, 7]$$$. His final pill score is $$$$$$ 1 \cdot (0 - 0) + 2 \cdot (1 - 0) + 3 \cdot (7 - 1) = 20. $$$$$$
In the second test case, he can publish the drafts with ratings $$$[0, -4, 10]$$$. The second post deducts points, but the third post more than makes up for it. His final pill score is $$$$$$ 1 \cdot (0 - 0) + 2 \cdot (-4 - 0) + 3 \cdot (10 - (-4)) = 34. $$$$$$