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.*;
import java.util.*;

public class Solution {

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int t = input.nextInt();
        for(int a = 0; a < t; a++) {
            int n = input.nextInt();
            int k = input.nextInt();
            int[] nums = new int[n];
            for(int i = 0; i < n; i++) {
                nums[i] = input.nextInt();
            }
            int answer = 0;
            int pos = 0;
            boolean possible = true;
            while(true) {
                int nextpos = pos;
                for(int i = nextpos; i < n; i++) {
                    if(nums[i] > k) {
                        nextpos = i;
                        break;
                    }
                }
                for(int i = pos; i < nextpos; i++) {
                    try {
                        if(nums[i - 1] > nums[i]) {
                            possible = false;
                            break;
                        }
                    } catch(Exception e) {}
                }
                if(!possible) {
                    break;
                }
                boolean sorted = true;
                for(int i = nextpos; i < n; i++) {
                    try {
                        if(nums[i - 1] > nums[i]) {
                            sorted = false;
                            break;
                        }
                    } catch(Exception e) {}
                }
                if(sorted) {
                    break;
                }
                if(nums[nextpos] <= k) {
                    possible = false;
                    break;
                }
                int temp = nums[nextpos];
                nums[nextpos] = k;
                k = temp;
                answer++;
                pos = nextpos;
            }
            if(possible) {
                System.out.println(answer);
            } else System.out.println(-1);
        }
    }
}