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.*;

public class Main {
    public static void main(String args[]) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int q=Integer.parseInt(br.readLine());

        for(int t=0;t<q;t++){

            String s = br.readLine();
            String[] s1 = s.split(" ");

            int n=Integer.parseInt(s1[0]);
            int x=Integer.parseInt(s1[1]);

            s = br.readLine();
            s1 = s.split(" ");
            int[] arr = new int[n];
            int[] brr = new int[n];

            for(int i=0;i<n;i++)
            {
                arr[i]=Integer.parseInt(s1[i]);
                brr[i]=arr[i];
            }

            int a=0,b=1,count=0;
            boolean found=false;

            for(int i=1;i<n;i++){

                if(arr[i]<arr[i-1]){

                    for(int j=a;j<i;j++){

                        if(arr[j]>x){
                            int temp = x;
                            x=arr[j];
                            arr[j]=temp;
                            found=true;
                            count++;
                        }
                    }

                   if(found){
                       i--;
                       a++;
                       found=false;
                   }else{
                       count=-1;
                       break;
                   }
                }
            }

            System.out.println(count);

        }
    }
}


