[Sakuzyo - Imprinting](https://www.youtube.com/watch?v=55Ca6av1kAY)

A.R.C. Markland-N is a tall building with n floors numbered from 1 to n. 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 s of the building. On each floor (including floor s, of course), there is a restaurant offering meals. However, due to renovations being in progress, k 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 t (1 ≤ t ≤ 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 ≤ n ≤ 10^9, 1 ≤ s ≤ n, 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 k distinct integers a_1, a_2, …, a_k (1 ≤ a_i ≤ 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.

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


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.
import java.util.*;
import java.lang.*;
import java.io.*;  
public class Main 
{
/*
    HashMap<> map=new HashMap<>();
    TreeMap<> map=new TreeMap<>();
    map.put(p,map.getOrDefault(p,0)+1);
    for(Map.Entry<> mx:map.entrySet()){
          int v=mx.getValue(),k=mx.getKey();
    }
    ArrayList<Pair<Character,Integer>> l=new ArrayList<>();
    ArrayList<> l=new ArrayList<>();
    HashSet<> has=new HashSet<>();*/
    PrintWriter out;
    FastReader sc;
    int mod=(int)(1e9+7); 
    public void sol(){
          int t=ni();
          while(t-->0){
                int n=ni(),s=ni(),k=ni();
                HashSet<Integer> h=new HashSet<>();
                for(int i=0;i<k;i++){
                      int p=ni();
                      h.add(p);
                }if(!h.contains(s))pl("0");
                else{
                      int left=maxint(),right=maxint();
                      for(int i=s+1;i<=n;i++){
                            if(!h.contains(i)){
                                  right=i;
                                  break;
                            }
                      }for(int i=s-1;i>=1;i--){
                            if(!h.contains(i)){
                                  left=i;
                                  break;
                            }
                      }if(left==maxint())pl(right-s);
                      else if(right==maxint())pl(s-left);
                      else
                      pl(min(s-left,right-s));
                }
          }
    }
    public static void main(String[] args) 
	{ 
	      Main g=new Main();
		g.out=new PrintWriter(System.out);
		g.sc=new FastReader();
		g.sol();
		g.out.flush();
	}
	static class FastReader 
	{ 
		BufferedReader br; 
		StringTokenizer st; 
 
		public FastReader() 
		{ 
			br = new BufferedReader(new
					InputStreamReader(System.in)); 
		} 
 
		String next() 
		{ 
			while (st == null || !st.hasMoreElements()) 
			{ 
				try
				{ 
					st = new StringTokenizer(br.readLine()); 
				} 
				catch (IOException e) 
				{ 
					e.printStackTrace(); 
				} 
			} 
			return st.nextToken(); 
		} 
 
		int nextInt() 
		{ 
			return Integer.parseInt(next()); 
		} 
 
		long nextLong() 
		{ 
			return Long.parseLong(next()); 
		} 
 
		double nextDouble() 
		{ 
			return Double.parseDouble(next()); 
		} 
 
		String nextLine() 
		{ 
			String str = ""; 
			try
			{ 
				str = br.readLine(); 
			} 
			catch (IOException e) 
			{ 
				e.printStackTrace(); 
			} 
			return str; 
		} 
	} public int ni(){
	      return sc.nextInt();
	}public long nl(){
	      return sc.nextLong();
	}public double nd(){
	      return sc.nextDouble();
	}public char[] rl(){
	      return sc.nextLine().toCharArray();
	}public String rl1(){
	      return sc.nextLine();
	}
	public void pl(Object s){
	      out.println(s);
	}public void ex(){
	      out.println();
	}
	public void pr(Object s){
	      out.print(s);
	}public String next(){
	      return sc.next();
	}public long abs(long x){
	      return Math.abs(x);
	}
	public int abs(int x){
	      return Math.abs(x);
	}
	public double abs(double x){
	      return Math.abs(x);
	}
      public long pow(long x,long y){
            return (long)Math.pow(x,y);
      }
      public int pow(int x,int y){
            return (int)Math.pow(x,y);
      }
      public double pow(double x,double y){
            return Math.pow(x,y);
      }public long min(long x,long y){
            return (long)Math.min(x,y);
      }
      public int min(int x,int y){
            return (int)Math.min(x,y);
      }
      public double min(double x,double y){
            return Math.min(x,y);
      }public static int gcd(int a, int b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}static void sort(int[] a) {
		ArrayList<Integer> l = new ArrayList<>();
		for (int i : a) {
			l.add(i);
		}
		Collections.sort(l);
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}void sort(long[] a) {
		ArrayList<Long> l = new ArrayList<>();
		for (long i : a) {
			l.add(i);
		}
		Collections.sort(l);
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}void sort(double[] a) {
		ArrayList<Double> l = new ArrayList<>();
		for (double i : a) {
			l.add(i);
		}
		Collections.sort(l);
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}int  swap(int a,int b){
	      return a;
	}long  swap(long a,long b){
	      return a;
	}double  swap(double a,double b){
	      return a;
	}
	boolean isPowerOfTwo (int x) 
      { 
            return x!=0 && ((x&(x-1)) == 0);     
      }boolean isPowerOfTwo (long x) 
      { 
            return x!=0 && ((x&(x-1)) == 0);     
      }public long max(long x,long y){
            return (long)Math.max(x,y);
      }
      public int max(int x,int y){
            return (int)Math.max(x,y);
      }
      public double max(double x,double y){
            return Math.max(x,y);
      }long sqrt(long x){
            return (long)Math.sqrt(x);
      }int sqrt(int x){
            return (int)Math.sqrt(x);
      }void input(int[] ar,int n){
            for(int i=0;i<n;i++)ar[i]=ni();
      }void input(long[] ar,int n){
            for(int i=0;i<n;i++)ar[i]=nl();
      }int maxint(){
            return Integer.MAX_VALUE;
      }int minint(){
            return Integer.MIN_VALUE;
      }long maxlong(){
            return Long.MAX_VALUE;
      }long minlong(){
            return Long.MIN_VALUE;
      }void fill(int[] ar,int k){
            Arrays.fill(ar,k);
      }void yes(){
            pl("YES");
      }void no(){
            pl("NO");
      }
    void sieve(int n) 
    { 
        boolean prime[] = new boolean[n+1]; 
        for(int i=0;i<=n;i++) 
            prime[i] = true; 
          
        for(int p = 2; p <=n; p++) 
        { 
            if(prime[p] == true) 
            { 
               // sieve[p]=p;
                for(int i = p*2; i <= n; i += p) {
                    prime[i] = false; 
                  //  sieve[i]=p;
                }
            } 
        }
    } 
      public static class pair implements Comparable<pair> {
		int x;
		int y;
 
		public pair(int x, int y) {
			this.x = x;
			this.y = y;
		}
 
		public String toString() {
			return x + "," + y;
		}
 
		public boolean equals(Object o) {
			if (o instanceof pair) {
				pair p = (pair) o;
				return p.x == x && p.y == y;
			}
			return false;
		}
 
		public int hashCode() {
			return new Double(x).hashCode() * 31 + new Double(y).hashCode();
		}
 
		public int compareTo(pair other) {
			if (this.x == other.x) {
				return Long.compare(this.y, other.y);
			}
			return Long.compare(this.x, other.x);
		}
      }
	 
} 