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.*;
import java.lang.*;

public class Main{
	static Scanner scanner = new Scanner(System.in);
	public static boolean s(int arr[]) {//判断数组是否有序
		for(int i = 0;i<arr.length-1;i++) {
			if(arr[i] > arr[i+1]) return true;
		}
		return false;
	}
	public static void main(String[] args) {
		int t = scanner.nextInt();
		for(int tt = 0;tt<t;tt++) {			
			show();		
		}
	}
	private static void show() {
		int n = scanner.nextInt(), x = scanner.nextInt();
		int arr[] = new int[n];
		for(int i = 0;i<n;i++) arr[i] = scanner.nextInt();			
		int i = 0;
		int ans = 0;
		while(s(arr)) {
			if(arr[i] > x) {
				int temp = x;
				x = arr[i];
				arr[i] = temp;
				ans++;
			}
			i++;
			if(i>=n) {
				ans = -1;
				break;
			}
		}
		System.out.println(ans);	
	}
}
