[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.io.Writer;
import java.io.BufferedWriter;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.*;
import java.io.*;
import java.math.*;

public class A1293{
  static class ProblemSolver{
    public void solveTheProblem(InputReader in,OutputWriter out, NumberTheory nt){
      int test=in.nextInt();
      while(test-- >0){
        Long n=in.nextLong();
        Long s=in.nextLong();
        Long k=in.nextLong();

        HashSet<Long> hs= new HashSet<>();
        for(int i=0;i<k;i++){
          hs.add(in.nextLong());
        }
        int c=1;
        while(true){
          if(!hs.contains(s)){
            System.out.println(0);
            break;
          }
          if((s+c)<=n && !hs.contains(s+c)){
            // System.out.println("--");
            System.out.println(c);
            break;
          }
          if((s-c)>0 && !hs.contains(s-c)){
            // System.out.println("==");
            System.out.println(c);
            break;
          }
          c++;
        }
      }
    }
  }

  public static void main(String[] args){
    InputStream inputStream=System.in;
    OutputStream outputStream=System.out;
    InputReader in=new InputReader(inputStream);
    OutputWriter out=new OutputWriter(outputStream);
    NumberTheory nt= new NumberTheory();
    ProblemSolver problemSolver=new ProblemSolver();
    problemSolver.solveTheProblem(in,out, nt);
    out.flush();
    out.close();
  }



  static class InputReader {
    private boolean finished = false;

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public InputReader(InputStream stream) {
      this.stream = stream;
    }

    public int read() {
      if (numChars == -1) {
        throw new InputMismatchException();
      }
      if (curChar >= numChars) {
        curChar = 0;
        try {
          numChars = stream.read(buf);
        } catch (IOException e) {
          throw new InputMismatchException();
        }
        if (numChars <= 0) {
          return -1;
        }
      }
      return buf[curChar++];
    }

    public int peek() {
      if (numChars == -1) {
        return -1;
      }
      if (curChar >= numChars) {
        curChar = 0;
        try {
          numChars = stream.read(buf);
        } catch (IOException e) {
          return -1;
        }
        if (numChars <= 0) {
          return -1;
        }
      }
      return buf[curChar];
    }

    public int nextInt() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      int res = 0;
      do {
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c - '0';
        c = read();
      } while (!isSpaceChar(c));
      return res * sgn;
    }

    public long nextLong() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      long res = 0;
      do {
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c - '0';
        c = read();
      } while (!isSpaceChar(c));
      return res * sgn;
    }

    public String nextLine() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      StringBuilder res = new StringBuilder();
      do {
        if (Character.isValidCodePoint(c)) {
          res.appendCodePoint(c);
        }
        c = read();
      } while (!isSpaceChar(c));
      return res.toString();
    }

    public boolean isSpaceChar(int c) {
      if (filter != null) {
        return filter.isSpaceChar(c);
      }
      return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private String readLine0() {
      StringBuilder buf = new StringBuilder();
      int c = read();
      while (c != '\n' && c != -1) {
        if (c != '\r') {
          buf.appendCodePoint(c);
        }
        c = read();
      }
      return buf.toString();
    }

    public String readLine() {
      String s = readLine0();
      while (s.trim().length() == 0) {
        s = readLine0();
      }
      return s;
    }

    public String readLine(boolean ignoreEmptyLines) {
      if (ignoreEmptyLines) {
        return readLine();
      } else {
        return readLine0();
      }
    }

    public BigInteger readBigInteger() {
      try {
        return new BigInteger(nextLine());
      } catch (NumberFormatException e) {
        throw new InputMismatchException();
      }
    }

    public char nextCharacter() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      return (char) c;
    }

    public double nextDouble() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      double res = 0;
      while (!isSpaceChar(c) && c != '.') {
        if (c == 'e' || c == 'E') {
          return res * Math.pow(10, nextInt());
        }
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c - '0';
        c = read();
      }
      if (c == '.') {
        c = read();
        double m = 1;
        while (!isSpaceChar(c)) {
          if (c == 'e' || c == 'E') {
            return res * Math.pow(10, nextInt());
          }
          if (c < '0' || c > '9') {
            throw new InputMismatchException();
          }
          m /= 10;
          res += (c - '0') * m;
          c = read();
        }
      }
      return res * sgn;
    }

    public boolean isExhausted() {
      int value;
      while (isSpaceChar(value = peek()) && value != -1) {
        read();
      }
      return value == -1;
    }

    public String next() {
      return nextLine();
    }

    public SpaceCharFilter getFilter() {
      return filter;
    }

    public void setFilter(SpaceCharFilter filter) {
      this.filter = filter;
    }

    public interface SpaceCharFilter {
      public boolean isSpaceChar(int ch);
    }
    public int[] nextIntArray(int n){
      int[] array=new int[n];
      for(int i=0;i<n;++i)array[i]=nextInt();
      return array;
    }
    public int[] nextSortedIntArray(int n){
      int array[]=nextIntArray(n);
      Arrays.sort(array);
      return array;
    }
    public ArrayList<Integer> nextIntArrayList(int n){
      ArrayList<Integer> ar= new ArrayList<>();
      for(int i=0;i<n;i++)
        ar.add(nextInt());
      return ar;
    }
		public ArrayList<Long> nextLongArrayList(int n){
      ArrayList<Long> ar= new ArrayList<>();
      for(int i=0;i<n;i++)
        ar.add(nextLong());
      return ar;
    }

    public int[] nextSumIntArray(int n){
      int[] array=new int[n];
      array[0]=nextInt();
      for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
      return array;
    }
    public long[] nextLongArray(int n){
      long[] array=new long[n];
      for(int i=0;i<n;++i)array[i]=nextLong();
      return array;
    }
    public long[] nextSumLongArray(int n){
      long[] array=new long[n];
      array[0]=nextInt();
      for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
      return array;
    }
    public long[] nextSortedLongArray(int n){
      long array[]=nextLongArray(n);
      Arrays.sort(array);
      return array;
    }
    public int[][] nextIntMatrix(int n,int m){
      int[][] matrix=new int[n][m];
      for(int i=0;i<n;++i)
      for(int j=0;j<m;++j)
      matrix[i][j]=nextInt();
      return matrix;
    }

    public int[][] nextIntMatrix(int n){
      return nextIntMatrix(n,n);
    }

    public long[][] nextLongMatrix(int n,int m){
      long[][] matrix=new long[n][m];
      for(int i=0;i<n;++i)
      for(int j=0;j<m;++j)
      matrix[i][j]=nextLong();
      return matrix;
    }

    public long[][] nextLongMatrix(int n){
      return nextLongMatrix(n,n);
    }

    public char[][] nextCharMatrix(int n,int m){
      char[][] matrix=new char[n][m];
      for(int i=0;i<n;++i)
      matrix[i]=next().toCharArray();
      return matrix;
    }

    public char[][] nextCharMatrix(int n){
      return nextCharMatrix(n,n);
    }
  }

  static class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
      writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
      this.writer = new PrintWriter(writer);
    }

    // public void print(char[] array) {
    //     writer.print(array);
    // }

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void print(int[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(double[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(long[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(char[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(String[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(int[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(double[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(long[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(char[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(String[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void println(int[] array) {
      print(array);
      writer.println();
    }

    public void println(double[] array) {
      print(array);
      writer.println();
    }

    public void println(long[] array) {
      print(array);
      writer.println();
    }

    // public void println(char[] array) {
    //     print(array);
    //     writer.println();
    // }

    public void println(String[] array) {
      print(array);
      writer.println();
    }

    public void println() {
      writer.println();
    }

    public void println(Object... objects) {
      print(objects);
      writer.println();
    }

    public void print(char i) {
      writer.print(i);
    }

    public void println(char i) {
      writer.println(i);
    }

    public void println(char[] array) {
      writer.println(array);
    }

    public void printf(String format, Object... objects) {
      writer.printf(format, objects);
    }

    public void close() {
      writer.close();
    }

    public void flush() {
      writer.flush();
    }

    public void print(long i) {
      writer.print(i);
    }

    public void println(long i) {
      writer.println(i);
    }

    public void print(int i) {
      writer.print(i);
    }

    public void println(int i) {
      writer.println(i);
    }

    public void separateLines(int[] array) {
      for (int i : array) {
        println(i);
      }
    }
  }
  static class NumberTheory{

      /**
       * Modular Arithmetic:
       *  1. (a+b)%c=(a%c+b%c)%c
       *  2. (a*b)%c=(a%c*b%c)%c
       *  3. (a-b)%c=(a%c-b%c+c)%c
       *  4. (a/b)%c=(a%c*(b^-1)%c)%c -- (b^-1 is multiplicative modulo inverse)
       */
      //Modular Addition
      public int modularAddition(int a,int b,int MOD){
          return (a%MOD+b%MOD)%MOD;
      }
      public long modularAddition(long a,long b,long MOD){
          return (a%MOD+b%MOD)%MOD;
      }
      //Modular Multiplication
      public int modularMultiplication(int a,int b,int MOD){
          return ((a%MOD)*(b%MOD))%MOD;
      }
      public long modularMultiplication(long a,long b,long MOD){
          return ((a%MOD)*(b%MOD))%MOD;
      }
      //Modular Subtraction
      public int modularSubtraction(int a,int b,int MOD){
          return (a%MOD-b%MOD+MOD)%MOD;
      }
      public long modularSubtraction(long a,long b,long MOD){
          return (a%MOD-b%MOD+MOD)%MOD;
      }

      /**
       * Binary Exponentiation
       */
      public int binaryExponentiation(int x,int n){
          if(n==0)return 1;
          else if(n%2==0)return binaryExponentiation(x*x,n/2);
          else return x*binaryExponentiation(x*x,(n-1)/2);
      }
      public long binaryExponentiation(long x,long n){
          long result=1;
          while(n>0){
              if(n%2==1)result*=x;
              x=x*x;
              n/=2;
          }
          return result;
      }

      /**
       * Modular Exponentiation
       */
      public int modularExponentiation(int x,int n,int MOD){
          if(n==0)return 1%MOD;
          else if(n%2==0)return modularExponentiation(modularMultiplication(x,x,MOD),n/2,MOD);
          else return modularMultiplication(x,modularExponentiation(modularMultiplication(x,x,MOD),(n-1)/2,MOD),MOD);
      }
      public long modularExponentiation(long x,long n,long MOD){
          long result=1;
          while(n>0){
              if(n%2==1)result=modularMultiplication(result,x,MOD);
              x=modularMultiplication(x,x,MOD);
              n/=2;
          }
          return result;
      }

      /**
       * Factorial of a number
       */
      public long factorials(long n){
          if(n==0)return 1;
          return n*factorials(n-1);
      }

      /**
       * Prime factors of a number
       */
      public ArrayList<Integer> distinctPrimeFactors(int n){
          ArrayList<Integer> factorials=new ArrayList<>();
          int limit=(int)Math.sqrt(n);
          if(n%2==0){
              factorials.add(2);
              while(n%2==0)n/=2;
          }
          for(int i=3;i<=limit;i+=2){
              if(n%i==0){
                  factorials.add(i);
                  while(n%i==0)n/=i;
              }
          }
          if(n>2)factorials.add(n);
          return factorials;
      }

      public ArrayList<Long> distinctPrimeFactors(long n){
          ArrayList<Long> factorials=new ArrayList<>();
          long limit=(long)Math.sqrt(n);
          if(n%2==0){
              factorials.add((long)2);
              while(n%2==0)n/=2;
          }
          for(long i=3;i<=limit;i+=2){
              if(n%i==0){
                  factorials.add(i);
                  while(n%i==0)n/=i;
              }
          }
          if(n>2)factorials.add(n);
          return factorials;
      }

      public ArrayList<Integer> primeFactors(int n){
          ArrayList<Integer> factorials=new ArrayList<>();
          int limit=(int)Math.sqrt(n);
          if(n%2==0){
              factorials.add(2);
              while(n%2==0)n/=2;
          }
          for(int i=3;i<=limit;i+=2){
              if(n%i==0){
                  factorials.add(i);
                  while(n%i==0)n/=i;
              }
          }
          if(n>2)factorials.add(n);
          return factorials;
      }

      public ArrayList<Long> primeFactors(long n){
          ArrayList<Long> factorials=new ArrayList<>();
          long limit=(long)Math.sqrt(n);
          if(n%2==0){
              factorials.add((long)2);
              while(n%2==0)n/=2;
          }
          for(long i=3;i<=limit;i+=2){
              if(n%i==0){
                  factorials.add(i);
                  while(n%i==0)n/=i;
              }
          }
          if(n>2)factorials.add(n);
          return factorials;
      }

      /**
       * Combination: nCr
       */
      //Naive version
      //(n,r)=(n-1,r-1)+(n-1,r) for r!=0 or r!=n
      //(n,0)=(n,n)=1
      public int binomialCoefficientRecursive(int n,int k){
          if(k==0 || k==n)return 1;//base case
          return binomialCoefficientRecursive(n-1,k-1)+binomialCoefficientRecursive(n-1,k);//recursion
      }

      //Dynamic Programming version(Uses bottom up approach to fill the table)
      //Time complexity: O(n*k)
      //Space complexity: O(n*k)
      public long binomialCoefficientIterative(int n,int k){
          long[][] C=new long[n+1][k+1];
          for(int i=0;i<=n;++i){
              for(int j=0;j<=Math.min(n,k);++j){
                  if(j==0 || j==i)C[i][j]=1;
                  else C[i][j]=C[i-1][j-1]+C[i-1][j];
              }
          }
          return C[n][k];
      }

      //Pascal's Triangle version(Space efficient program)
      //Time complexity: O(n*k)
      //Space complexity: O(k)
      public long nCr(int n,int r){
          int[] C=new int[r+1];
          C[0]=1;//nC0=1
          for(int i=1;i<=n;++i)
              for(int j=Math.min(i,r);j>0;--j)
                  C[j]=C[j]+C[j-1];
          return C[r];
      }

      /**
       * Catlan number:
       *  - Time complexity: O(n*n)
       *  - Auxiliary space: O(n)
       *
       *  NOTE: Time complexity could be reduced to O(n) but it is
       *        possible if and only if n is small or else there is
       *        a chance of getting an overflow. To decrease the time
       *        complexity to O(n) just remember nCr=nCn-r
       */
      public long catlanNumber(int n){
          long[] catlan=new long[n+1];
          catlan[0]=catlan[1]=1;
          for(int i=2;i<=n;++i)
              for(int j=0;j<i;++j)
                  catlan[i]+=catlan[j]*catlan[i-1-j];

          return catlan[n];
      }

      /**
       * Greatest Common Divisor(GCD)
       *  - It is also known as Highest Common Factor(HCF)
       *  - Time complexity: log(min(a,b))
       *  - Auxiliary Space: O(1)
       */
      public int gcd(int a,int b){
          if(b==0)return a;
          return gcd(b,a %b);
      }

      public long gcd(long a,long b){
          if(b==0)return a;
          return gcd(b,a%b);
      }

      /**
       * Extended Euclid's Algorithm:
       *  - ax+by=gcd(a,b)
       *  - Time complexity:
       *  -
       */


      /**
       * Least Common Multiple(LCM):
       *  - Time complexity: log(min(a,b))
       *  - Auxiliary Space: O(1)
       */
      public long lcm(long a,long b){
          return (a*b)/gcd(a,b);
      }

  }
}
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//              ,I8 . . . .,I88I. . .i88888888888"
//             I8. . . .,mII88Ima. .i88888888888"
//            ,8"..,mI88I88I88I8Imi888888888888"
//            I8.,I8I"""        ""II88888888888
//           ;I8I8"                  ""I8888888
//           ""                         "I88888
//                                        "I888
//                                         "I88,
//                                          "I88
//                                           "88,
//                                            I88,              ______   __
//                           ______           "I88__        .mI88I88I88I88I88,
//                      .,mI88I88I88, ,mI88,   I88"""     ,mI8". . . . "I8,..8,
//                    ,I888' . . . "I88.\ "8,  I88      ,I8". . . .  / :;I8 \ 8,
//                  .mI8' . . .  / .:"I8.\ 88  "88,    ,8". . .  / .;mI8I8I8,\ 8
//                 ,I8'. . .  / . .:;,I8I8I888  I88   ,8". .  / .:mI8"'   "I8,:8
//                ,I8'. . . / . .:;,mI8"  `"I88 I88   I8. .  / .m8"         "I8I
//               ,I8 . .  / . .:;,mI8"      "I88888   88,.  / ,m8            "8'
//               I8'. .  / . .;,mI8"          "II888 ,I8I8,.,I8"
//               I8 . . / . .,mI8"              I8888888' """
//               `I8,.  / ;,mI8"                 II888
//                "I8I, /,mI8"                 __I888
//                  "I8888"                   """I88
//                    ""                         I88
//                                               I88__
//                                               I88"""
//                                               I88
//                                               I88
//                                             __I88
//                                            """I88
//                                               I88
//                                               I88
//                                               I88__
//                                               I88"""
//                                               I88
//                                        BITSY  ___  CHUCK
