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.*;
import java.util.*;
public class abc
{
    
    public static boolean sorted(int a[])
    {
         
         for(int i=1;i<a.length;i++)
         {
              if(a[i]<a[i-1])
              return false;
         }
         return true;
    }
     public static void main(String arg[])throws IOException
     {
          BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
          int t=Integer.parseInt(br.readLine());
          StringBuilder sb=new StringBuilder();
          while(t-->0)
          {
       String s[]=br.readLine().split(" ");
       int n=Integer.parseInt(s[0]);
       int x=Integer.parseInt(s[1]);
       s=br.readLine().split(" ");
       int a[]=new int[n];
       for(int i=0;i<n;i++)
       {
            a[i]=Integer.parseInt(s[i]);
       }
       boolean bi=true;
       for(int i=1;i<n;i++)
       {
            if(a[i]<a[i-1])
            {
                 bi=false;
                 break;
            }
       }
       int ans=0;
       if(bi)
       sb.append(String.valueOf(ans)+"\n");
      else
      {
           bi=false;
           for(int i=0;i<n;i++)
           {
                if(x<a[i])
                {
                     int t1=a[i];
                     a[i]=x;
                     x=t1;
                     ans++;
                }
                if(sorted(a))
                {
                     bi=true;
                    break; 
                }
           }
           if(bi)
           sb.append(String.valueOf(ans)+"\n");
           else
           sb.append("-1\n");
      }
     }
     System.out.println(sb);
}
}