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

A.R.C. Markland-N is a tall building with nn floors numbered from 11 to nn. Between each two adjacent floors in the building, there is a staircase connecting them.

It’s lunchtime for our sensei Colin “ConneR” Neumann Jr, and he’s planning for a location to enjoy his meal.

ConneR’s office is at floor ss of the building. On each floor (including floor ss, of course), there is a restaurant offering meals. However, due to renovations being in progress, kk of the restaurants are currently closed, and as a result, ConneR can’t enjoy his lunch there.

CooneR wants to reach a restaurant as quickly as possible to save time. What is the minimum number of staircases he needs to walk to reach a closest currently open restaurant.

Please answer him quickly, and you might earn his praise and even enjoy the lunch with him in the elegant Neumanns’ way!

Input

The first line contains one integer tt (1≤t≤10001≤t≤1000) — the number of test cases in the test. Then the descriptions of tt test cases follow.

The first line of a test case contains three integers nn, ss and kk (2≤n≤1092≤n≤109, 1≤s≤n1≤s≤n, 1≤k≤min(n−1,1000)1≤k≤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 kk distinct integers a1,a2,…,aka1,a2,…,ak (1≤ai≤n1≤ai≤n) — the floor numbers of the currently closed restaurants.

It is guaranteed that the sum of kk over all test cases does not exceed 10001000.

Output

For each test case print a single integer — the minimum number of staircases required for ConneR to walk from the floor ss 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 44.

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 66-th floor.

题目大意：

有一栋 n 层高且每层都有餐厅的楼，有一个人在 s 层要去吃饭儿，给出 k 个关门的餐厅的层数，问这人最少走多少层能吃着饭儿。

解题思路：

k 的范围是从 （n-1）到 1000，从 s 层开始向上下两侧枚举，记录下第一个可行的距离比较。

代码如下：

#include
#include//借用map函数解决数组太大无法标记的问题
using namespace std;
int t,n,s,k;//t为测试用例数n为楼层数s为人所在楼层位置k为关闭餐厅数
void main()
{
	cin>>t;
	while(t--){
		map<int,int>m;int x;
		scanf("%d%d%d",&n,&s,&k);
		for(int i=1;i<=k;i++){//遍历楼层
			scanf("%d",&x);
			m[x]=1;//记录位置
		}
		for(int i=0;i<=n;i++)
			if((!m[s-i]&&s-i>=1)||(!m[s+i]&&s+i<=n)){//为可行位置
				printf("%d\n",i);
				break;
			}
	}
}