[codeforces 1293A] ConneR and the A.R.C. Markland-N

题目：http://codeforces.com/problemset/problem/1293/A

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.

Example

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

Output

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.

题意：有n个楼层（从1到n），每个楼层都有餐厅能吃饭，ConneR在s层，现在有k个楼层餐厅是关门的（不超出1000），问ConneR最少要一栋多少层

分析：n很大，但是k超过1000，所以要从k下手，我刚开始理解的不太清楚用数组a【1100】来记录k个数，来一个a【k】=1，结果数组越界了（n很大），解决办法是用map<int,int>来记录，后面只需暴力从s向两边搜索即可

代码：

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstdlib>
#include <cstring>
#include <map>
using namespace std;int t,n,s,k;
int main(){cin>>t;while(t--){map<int,int> a;cin>>n>>s>>k;a.clear();for(int i=0;i<k;i++){int g;cin>>g;a[g]=1;}int step = 0;while(1){if(s+step<=n&&a[s+step]==0)  break;if(s-step>0&&a[s-step]==0) break;step++;}cout<<step<<endl;}
}

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