ConneR and the A.R.C. Markland-N

Description:

Input:

The first line contains one integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases in the test. Then the descriptions of $$$t$$$ test cases follow.

The first line of a test case contains three integers $$$n$$$, $$$s$$$ and $$$k$$$ ($$$2 \le n \le 10^9$$$, $$$1 \le s \le n$$$, $$$1 \le k \le \min(n-1, 1000)$$$) — respectively the number of floors of A.R.C. Markland-N, the floor where ConneR is in, and the number of closed restaurants.

The second line of a test case contains $$$k$$$ distinct integers $$$a_1, a_2, \ldots, a_k$$$ ($$$1 \le a_i \le n$$$) — the floor numbers of the currently closed restaurants.

It is guaranteed that the sum of $$$k$$$ over all test cases does not exceed $$$1000$$$.

Output:

For each test case print a single integer — the minimum number of staircases required for ConneR to walk from the floor $$$s$$$ to a floor with an open restaurant.

Sample Input:

5
5 2 3
1 2 3
4 3 3
4 1 2
10 2 6
1 2 3 4 5 7
2 1 1
2
100 76 8
76 75 36 67 41 74 10 77

Sample Output:

2
0
4
0
2

Note:

In the first example test case, the nearest floor with an open restaurant would be the floor $$$4$$$.

In the second example test case, the floor with ConneR's office still has an open restaurant, so Sensei won't have to go anywhere.

In the third example test case, the closest open restaurant is on the $$$6$$$-th floor.