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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class D {
  private static final Scanner in = new Scanner(System.in);
  private static final PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

  public static void main(String[] args) {
    Solver solver = new Solver();
    solver.solve();
    out.close();
  }

  private static class Solver {
    private void solve() {
      int t = in.nextInt();
      while (t-- > 0) {
        solveOne();
      }
    }

    private void solveOne() {
      int n = in.nextInt();
      int x = in.nextInt();
      int[] a = new int[n + 1];
      for (int i = 1; i <= n; i++) {
        a[i] = in.nextInt();
      }
      int[][][] p = new int[n + 1][501][501];
      for (int i = 0; i <= n; i++) {
        for (int j = 0; j <= 500; j++) {
          for (int k = 0; k <= 500; k++) {
            p[i][j][k] = Integer.MAX_VALUE;
          }
        }
      }
      p[0][0][x] = 0;
      for (int i = 1; i <= n; i++) {
        for (int j = 0; j <= 500; j++) {
          for (int k = 0; k <= 500; k++) {
            if (p[i - 1][j][k] < Integer.MAX_VALUE) {
              if (a[i] >= j) {
                p[i][a[i]][k] = Math.min(p[i][a[i]][k], p[i - 1][j][k]);
              }
              if (k >= j && a[i] > k) {
                p[i][k][a[i]] = Math.min(p[i][k][a[i]], p[i - 1][j][k] + 1);
              }
            }
          }
        }
      }
      int ans = Integer.MAX_VALUE;
      for (int j = 0; j <= 500; j++) {
        for (int k = 0; k <= 500; k++) {
          ans = Math.min(ans, p[n][j][k]);
        }
      }
      out.println(ans == Integer.MAX_VALUE ? -1 : ans);
    }
  }

  public static class Scanner {
    private final BufferedReader br;
    private StringTokenizer st;

    public Scanner(InputStream in) {
      br = new BufferedReader(new InputStreamReader(in));
    }

    String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          st = new StringTokenizer(br.readLine());
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return st.nextToken();
    }

    int nextInt() {
      return Integer.parseInt(next());
    }

    long nextLong() {
      return Long.parseLong(next());
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    String nextLine() {
      try {
        return br.readLine();
      } catch (IOException e) {
        throw new RuntimeException(e);
      }
    }
  }
}