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.File;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.*;

public class Main
{
    
    public static boolean IsSorted(int a[])
    {
        boolean check = true;
        for (int i = 0; i < a.length-1; i++) {
            if(a[i]>a[i+1])
            {
                check = false;
                break;
            }
        }
        return check;
        
    }
    
    public static void main(String[] args)
    {
        Scanner input = new Scanner(System.in);
       int tc = input.nextInt();
       while(tc-->0)
       {
           int n = input.nextInt();
       int x = input.nextInt();
       int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = input.nextInt();
        }
        int count=0;
        
            while(!IsSorted(a))
            {
                count++;
                int i =0;
                while(i<n&&a[i]<=x)
                {
                    i++;
                }
                if(i==n)
                {
                  count=-1; 
                   break;
                }
                    
                int temp = a[i];
                a[i] = x;
                x = temp;
                
            }
            
        
        System.out.println(count);
       }
    }
   
}