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.Scanner;

public class SequenceAndSwap {
	
	   public static boolean isSorted(int[] arr) {
	       for (int i = 0; i < arr.length-1; i++) {
	          if (arr[i] > arr[i+1])
	              return false;
	       }
	       return true;
	   }

	public static void main(String[] args) {
		// TODO Auto-generated method stub
     Scanner sc = new Scanner(System.in);
     int t = sc.nextInt();
     while(t-->0) {
    	 int n = sc.nextInt();
    	 int x = sc.nextInt();
    	 int a[] = new int[n];
    	 for(int i=0;i<n;i++) {
    		 a[i]=sc.nextInt();
    	 }
    	 int count =0;
    	 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);
    	 }
     
     }
    	
    		 
     }
	

}