[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.
   // package com.company;
    import java.io.BufferedReader;
    import java.io.IOException;
    import java.io.InputStreamReader;
    import java.lang.reflect.Array;
    import java.sql.SQLOutput;
    import java.util.*;
    public class Main {

        public static void main(String[] args) throws IOException {
//           Scanner s = new Scanner(System.in);
  BufferedReader s=new BufferedReader(new InputStreamReader(System.in));
              StringBuilder sb = new StringBuilder();//int n=Integer.parseInt(s.readLine());

        int t=Integer.parseInt(s.readLine());
        while(t-->0){
          String[] str=s.readLine().trim().split("\\s+");
            int n=Integer.parseInt(str[0]);
            int s1=Integer.parseInt(str[1]);
            int k=Integer.parseInt(str[2]);
            int[] a=new int[k];
           HashMap<Integer,Integer> h=new HashMap<Integer, Integer>();
            String[] str1=s.readLine().trim().split("\\s+");

            for(int i=0;i<k;i++){
                a[i]=Integer.parseInt(str1[i]);

                h.put(a[i],1);

           }Arrays.sort(a);
         if(!h.containsKey(s1)){
             System.out.println(0);
         }else{
           int low=0;int high=k-1;int ind=0;
           while(low<=high){
               int mid=(low+high)/2;
               if(a[mid]==s1){
                   ind=mid;break;
               }else if(a[mid]>s1){
                   high=mid-1;
               }else{
                   low=mid+1;
               }
           }int j=0;int min=Integer.MAX_VALUE;
        for(int i=ind;i>=0;i--){
               if(a[i]!=a[ind]-j){
            //       System.out.println(a[i]);

                   min=Math.min(min,Math.abs(s1-a[ind]+j));      break;
               }j++;
        } j=0;for(int i=ind;i<k;i++){
                if(a[i]!=a[ind]+j){
             //     System.out.println(a[i]);
                    min=Math.min(min,Math.abs(s1-a[ind]-j));break;
                }j++;
            }{
            if(a[0]>1)
            min=Math.min(min,a[ind]-a[0]+1);
                 if(a[k-1]<n){
                     min=Math.min(min,a[k-1]+1-a[ind]);
                 }
        }
            System.out.println(min);
        }}
       //     System.out.println(min);
        }
        static  void computeLPSArray(String pat, int M, int lps[])
        {
            int len = 0;
            int i = 1;
            lps[0] = 0;
            while (i < M) {
                if (pat.charAt(i) == pat.charAt(len)) {
                    len++;
                    lps[i] = len;
                    i++;
                }
                else // (pat[i] != pat[len])
                {
                    if (len != 0) {
                        len = lps[len - 1];
   }
                    else // if (len == 0)
                    {
                        lps[i] = len;
                        i++;
                    }
                }
            }
        }
        static boolean isPrime(int n)
        {
            // Corner cas
            if (n <= 1) return false;
            if (n <= 3) return true;

            // This is checked so that we can skip
            // middle five numbers in below loop
            if (n % 2 == 0 || n % 3 == 0) return false;

            for (int i = 5; i * i <= n; i = i + 6)
                if (n % i == 0 || n % (i + 2) == 0)
                    return false;

            return true;
        }
        static boolean isPrime(int n, int k)
        {
            // Corner cases
            if (n <= 1 || n == 4) return false;
            if (n <= 3) return true;

            // Try k times
            while (k > 0)
            {
                // Pick a random number in [2..n-2]
                // Above corner cases make sure that n > 4
                int a = 2 + (int)(Math.random() % (n - 4));

                // Fermat's little theorem
                if (power(a, n - 1, n) != 1)
                    return false;

                k--;
            }

            return true;
        }
        static double power(double x, long y, int p) {
            double res = 1;
            x = x % p;
            while (y > 0) {
                if ((y & 1) == 1)
                    res = (res * x) % p;
                y = y >> 1;
                x = (x * x) % p;
            }
            return res;
        }
        public static void fracion(double x) {
            String a = "" + x;
            String spilts[] = a.split("\\."); // split using decimal
            int b = spilts[1].length(); // find the decimal length
            int denominator = (int) Math.pow(10, b); // calculate the denominator
            int numerator = (int) (x * denominator); // calculate the nerumrator Ex
            // 1.2*10 = 12
            int gcd = (int)gcd((long)numerator, denominator); // Find the greatest common
            // divisor bw them
            String fraction = "" + numerator / gcd + "/" + denominator / gcd;
            // System.out.println((denominator/gcd));
            long x1=modInverse(denominator / gcd,998244353  );
            //  System.out.println(x1);
            System.out.println((((numerator / gcd )%998244353 *(x1%998244353  ))%998244353  ) );
        }static int max=Integer.MIN_VALUE;
static int max1=Integer.MIN_VALUE;static long[][] dp;static int[][] c;static int k=1;static int bhoo=0;
static int[] car;static int ans;static HashMap<Integer,Integer>[] ha;
public static void dfs(int ans2,int papa, int i, ArrayList<Integer>[] h, int[] vis,HashMap<Integer,Integer>[] bad) {
    vis[i] = 1;
    if(i!=1&&h[i].size()==1){
    if(ans2!=-1)  {ans++;  sb1.append(ans2+" ");}
    }
    if(h[i]==null) return;
int hu=0;int hai=0;
for(Integer j:h[i]){
    if(vis[j]==0&&bad[i].containsKey(j)) {
        hai=1;break;
    }
}int khi=0;
             for(Integer j:h[i]) {//if(vis[j]==0) flag=1;
                    if(vis[j]==0){
                        if(!bad[i].containsKey(j)){
                        if(hai==0&&khi==0){khi=1;    dfs(ans2,papa,j,h,vis,bad);}
                        else dfs(-1,papa,j,h,vis,bad);
                        }else{
                            if(hu==0){
                                if(papa==0){//ans++;//sb1.append(j+" ");
                                    dfs(j,1,j,h,vis,bad);
                                }else{
                                hu=1;
                                dfs( j,1,j,h,vis,bad);}
                            }else{
                            //    ans++;//sb1.append(j+" ");
                                dfs(j,1,j,h,vis,bad);
                            }
                        }
                    }
             }//if(flag==1) bhoo=-1;
        }static StringBuilder sb1=new StringBuilder();
        public static void bfs(int i, HashMap<Integer, Integer>[] h, int[] vis, int len, int papa) {
            Queue<Integer> q = new LinkedList<Integer>();
            q.add(i);
   }
      static int i(String a) {
            return Integer.parseInt(a);
        }
     static long l(String a) {
            return Long.parseLong(a);
        }
        static String[] inp() throws IOException {
            BufferedReader s = new BufferedReader(new InputStreamReader(System.in));
            return s.readLine().trim().split("\\s+");
        }


        static long gcd(long a, long b) {
            if (b == 0)
                return a;
            return gcd(b, a % b);
        }
        static long modInverse(int a, int m)
        {


            {
                // If a and m are relatively prime, then modulo inverse
                // is a^(m-2) mode m
                return (power(a, m - 2, m));
            }
        }

        // To compute x^y under modulo m
        static long power(int x, int y, int m)
        {
            if (y == 0)
                return 1;

            long p = power(x, y / 2, m) % m;
            p = (p * p) % m;

            if (y % 2 == 0)
                return p;
            else
                return (x * p) % m;
        }

        // Function to return gcd of a and b

    }
    class Student
    {
        int l;int r;int i;
        public Student(int l, int r,int i) {
            this.l = l;
            this.r = r;this.i=i;
        }
    // Constructor


        // Used to print student details in main()
        public String toString()
        {
            return this.l+" ";
        }
    }

    class Sortbyroll implements Comparator<Student>
    {
        // Used for sorting in ascending order of
        // roll number
        public int compare(Student a, Student b){
      return a.l-b.l;  }
    } class Sortbyroll1 implements Comparator<Student>
    {
        // Used for sorting in ascending order of
        // roll number
        public int compare(Student a, Student b){
        return a.l-b.l;
        }
    }