Insert a Progression

2000ms

262144K

Description:

You are given a sequence of $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$. You are also given $$$x$$$ integers $$$1, 2, \dots, x$$$.

You are asked to insert each of the extra integers into the sequence $$$a$$$. Each integer can be inserted at the beginning of the sequence, at the end of the sequence, or between any elements of the sequence.

The score of the resulting sequence $$$a'$$$ is the sum of absolute differences of adjacent elements in it $$$\left(\sum \limits_{i=1}^{n+x-1} |a'_i - a'_{i+1}|\right)$$$.

What is the smallest possible score of the resulting sequence $$$a'$$$?

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of testcases.

The first line of each testcase contains two integers $$$n$$$ and $$$x$$$ ($$$1 \le n, x \le 2 \cdot 10^5$$$) — the length of the sequence and the number of extra integers.

The second line of each testcase contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 2 \cdot 10^5$$$).

The sum of $$$n$$$ over all testcases doesn't exceed $$$2 \cdot 10^5$$$.

Output:

For each testcase, print a single integer — the smallest sum of absolute differences of adjacent elements of the sequence after you insert the extra integers into it.

Sample Input:

4
1 5
10
3 8
7 2 10
10 2
6 1 5 7 3 3 9 10 10 1
4 10
1 3 1 2

Sample Output:

Note:

Here are the sequences with the smallest scores for the example. The underlined elements are the extra integers. Note that there exist other sequences with this smallest score.

$$$\underline{1}, \underline{2}, \underline{3}, \underline{4}, \underline{5}, 10$$$
$$$\underline{7}, 7, \underline{6}, \underline{4}, 2, \underline{2}, \underline{1}, \underline{3}, \underline{5}, \underline{8}, 10$$$
$$$6, \underline{1}, 1, \underline{2}, 5, 7, 3, 3, 9, 10, 10, 1$$$
$$$1, 3, \underline{1}, 1, 2, \underline{2}, \underline{3}, \underline{4}, \underline{5}, \underline{6}, \underline{7}, \underline{8}, \underline{9}, \underline{10}$$$

Informação

Provedor Codeforces

Código CF1671D