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.util.*;
import java.lang.*;
import java.io.*;
public class Main
{
   public static boolean isSorted(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[] args) throws java.lang.Exception
	{
		Scanner sc=new Scanner(System.in);
		int t=sc.nextInt();
		while(t-->0) {
		    int n=sc.nextInt();
		    int x=sc.nextInt();
		    int count=0;
		    int a[]=new int[n];
		    for(int i=0;i<n;i++)
		    a[i]=sc.nextInt();
		    if(isSorted(a))
		    System.out.println("0");
		    else {
		    for(int i=0;i<n;i++) {
		        if(a[i]>x) {
		            int temp=a[i];
		            a[i]=x;
		            x=temp;
		            count++;
		        }
		         if(isSorted(a)) {
		         break;
		         }
		    }
		     if(isSorted(a))
		    System.out.println(count);
		   
		    else 
		    System.out.println("-1");
		}
		}
		
	}
}
