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
//created by Whiplash99
import java.io.*;
import java.util.*;
public class D
{
    private static boolean isSorted(int[] a, int N)
    {
        int i;
        for(i=1;i<N;i++) if(a[i]<a[i-1]) break;
        return i==N;
    }
    private static int getPos(int[] a, int N, int X)
    {
        int i;
        for(i=0;i<N;i++) if(a[i]>X) return i;
        return -1;
    }
    public static void main(String[] args) throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

        int i,N;

        int T=Integer.parseInt(br.readLine().trim());
        StringBuilder sb=new StringBuilder();

        while (T-->0)
        {
            String[] s=br.readLine().trim().split(" ");
            N=Integer.parseInt(s[0]);
            int X=Integer.parseInt(s[1]);

            int[] a=new int[N];
            s=br.readLine().trim().split(" ");
            for(i=0;i<N;i++) a[i]=Integer.parseInt(s[i]);

            if(isSorted(a,N))
            {
                sb.append(0).append("\n");
                continue;
            }

            int count=0;
            boolean flag=true;

            while (flag)
            {
                flag=false;
                int pos=getPos(a,N,X);
                if(pos==-1) break;

                count++; flag=true;
                int tmp=a[pos]; a[pos]=X; X=tmp;
                if(isSorted(a,N)) break;
            }

            if(isSorted(a,N)) sb.append(count).append("\n");
            else sb.append(-1).append("\n");
        }
        System.out.println(sb);
    }
}