A. Letter Home
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array of distinct integers $$$x_1, x_2, \ldots, x_n$$$ and an integer $$$s$$$.

Initially, you are at position $$$pos = s$$$ on the $$$X$$$ axis. In one step, you can perform exactly one of the following two actions:

  • Move from position $$$pos$$$ to position $$$pos + 1$$$.
  • Move from position $$$pos$$$ to position $$$pos - 1$$$.

A sequence of steps will be considered successful if, during the entire journey, you visit each position $$$x_i$$$ on the $$$X$$$ axis at least once. Note that the initial position $$$pos = s$$$ is also considered visited.

Your task is to determine the minimum number of steps in any successful sequence of steps.

Input

Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$s$$$ ($$$1 \leq n \leq 10$$$, $$$1 \leq s \leq 100$$$) — the number of positions to visit and the starting position.

The second line of each test case contains $$$n$$$ integers $$$x_1, x_2, \ldots, x_n$$$ ($$$1 \leq x_i \leq 100$$$). It is guaranteed that for all $$$1 \leq i \lt n$$$, it holds that $$$x_i \lt x_{i + 1}$$$.

Output

For each test case, output the minimum number of steps in any successful sequence of steps.

Example
Input
12
1 1
1
1 2
1
1 1
2
2 1
2 3
2 2
1 3
2 3
1 2
3 1
1 2 3
3 2
1 3 4
3 3
1 2 3
4 3
1 2 3 10
5 5
1 2 3 6 7
6 6
1 2 3 9 10 11
Output
0
1
1
2
3
2
2
4
2
11
8
15
Note

In the first test case, no steps need to be taken, so the only visited position will be $$$1$$$.

In the second test case, the following path can be taken: $$$2 \rightarrow 1$$$. The number of steps is $$$1$$$.

In the third test case, the following path can be taken: $$$1 \rightarrow 2$$$. The number of steps is $$$1$$$.

In the fifth test case, the following path can be taken: $$$2 \rightarrow 1 \rightarrow 2 \rightarrow 3$$$. The number of steps is $$$3$$$.