You are given a sequence a consisting of n integers a_1, a_2, ..., a_n, and an integer x. Your task is to make the sequence a sorted (it is considered sorted if the condition a_1 ≤ a_2 ≤ a_3 ≤ ... ≤ a_n holds).

To make the sequence sorted, you may perform the following operation any number of times you want (possibly zero): choose an integer i such that 1 ≤ i ≤ n and a_i > x, and swap the values of a_i and x.

For example, if a = [0, 2, 3, 5, 4], x = 1, the following sequence of operations is possible:

  1. choose i = 2 (it is possible since a_2 > x), then a = [0, 1, 3, 5, 4], x = 2; 
  2. choose i = 3 (it is possible since a_3 > x), then a = [0, 1, 2, 5, 4], x = 3; 
  3. choose i = 4 (it is possible since a_4 > x), then a = [0, 1, 2, 3, 4], x = 5. 



Calculate the minimum number of operations you have to perform so that a becomes sorted, or report that it is impossible.

Input

The first line contains one integer t (1 ≤ t ≤ 500) — the number of test cases.

Each test case consists of two lines. The first line contains two integers n and x (1 ≤ n ≤ 500, 0 ≤ x ≤ 500) — the number of elements in the sequence and the initial value of x.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 500).

The sum of values of n over all test cases in the input does not exceed 500.

Output

For each test case, print one integer — the minimum number of operations you have to perform to make a sorted, or -1, if it is impossible.

Example

Input


6
4 1
2 3 5 4
5 6
1 1 3 4 4
1 10
2
2 10
11 9
2 10
12 11
5 18
81 324 218 413 324


Output


3
0
0
-1
1
3

import java.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class D {
  static int inf = 1000_000_000;
  public static void main(String[] args) throws IOException {
    Scanner sc = new Scanner(System.in);
    PrintWriter pw = new PrintWriter(System.out);

    int tc = sc.nextInt();
    while(tc-->0) {
      int ans = inf;
      int n = sc.nextInt();
      int x = sc.nextInt();
      int[] orig = new int[n];
      int[] allNumbers = new int[n+1];
      for (int i = 0; i < n; i++) {
        orig[i] = sc.nextInt();
        allNumbers[i] = orig[i];
      }
      allNumbers[n] = x;
      Arrays.sort(allNumbers);

      for (int i = 0; i < allNumbers.length; i++) {
        int[] chosen = new int[n];
        int idx = 0;
        for (int j = 0; j < allNumbers.length; j++) {
          if (j != i)
            chosen[idx++] = allNumbers[j];
        }
        int out = allNumbers[i];

        ans = Math.min(ans, solve(out, x, chosen, orig.clone()));
      }
      pw.println(ans == inf?-1:ans);

    }

    pw.flush();
    pw.close();
  }

  public static int solve(int out, int x, int[] chosen, int[] orig) {
    int steps = 0;

    while (x < out) {
      // get pos
      int posx = -1;
      for (int i = 0; i < chosen.length; i++) {
        if(chosen[i] == x && orig[i] != x) {
          posx = i;
        }
      }

      // use pos
      if (orig[posx] <= x) {
        break;
      }

      int tmp = x;
      x = orig[posx];
      orig[posx] = tmp;
      steps++;
    }

    if(isSorted(orig))
      return steps;
    else
      return inf;
  }

  public static boolean isSorted(int[] arr) {
    for (int i = 0; i < arr.length-1; i++) {
      if (arr[i] > arr[i+1])
        return false;
    }
    return true;
  }

  static class Scanner
  {
    StringTokenizer st; BufferedReader br;
    public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}
    public Scanner(String s) throws FileNotFoundException {	br = new BufferedReader(new FileReader(new File(s)));}
    public String next() throws IOException {while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());return st.nextToken();}
    public int nextInt() throws IOException {return Integer.parseInt(next());}
    public long nextLong() throws IOException {return Long.parseLong(next());}
    public String nextLine() throws IOException {return br.readLine();}
    public boolean ready() throws IOException {return br.ready();}
  }
}
