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.io.*;
public class A {
    static PrintWriter ww = new PrintWriter(System.out);
    static boolean check(int arr[] , int i){
        while(i < arr.length - 1){
            if(arr[i] > arr[i + 1])return false;
            i++;
        }
        return true;
    }
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);

        int tt = sc.nextInt();
        sc.nextLine();
        
        while(tt -- >  0){
            int n = sc.nextInt();
            int x = sc.nextInt();
            
            int arr[] = new int[n];
            for(int i = 0 ; i < n ; i ++){
                arr[i] = sc.nextInt();
            }
            int res = 0;
            for(int i = 0 ; i < n ; i ++){
                if(check(arr , i))break;
                else if(x < arr[i]){
                    int temp = arr[i];
                    arr[i] = x;
                    x = temp;
                    res++;
                }
                else if(x == arr[i])continue;
                else if(x > arr[i]){
                    if(i > 0 && arr[i] < arr[i - 1]){
                        res = -1;
                        break;
                    }
                    else{
                        continue;
                    }
                }
            }
            if(!check(arr , 0))res = -1;
            ww.println(res);
        }
        ww.close();
    }    
}