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 sequences {
	public static void main(String [] args) throws Exception {
		Scanner in = new Scanner(System.in);
		int t = in.nextInt();
		for(int q=0;q<t;q++)
		{
			int n = in.nextInt();
			int x = in.nextInt();
			int count = 0;
			boolean flag = false;
			int[] arr = new int[n];
			for(int i=0;i<n;i++)
			{
				arr[i] = in.nextInt();
			}
			label:
			while(!sorted(arr))
			{
				for(int i=0;i<n;i++)
				{
					if(arr[i] > x)
					{
						int temp = arr[i];
						arr[i] = x;
						x = temp;
						//System.out.println(Arrays.toString(arr));
						count++;
						break;
					}
					if(i == n-1)
					{
						System.out.println(-1);
						flag = true;
						break label;
					}
					
				}
			}
			if(!flag)
			{
				System.out.println(count);
			}
			

		}
	}
	public static boolean sorted(int [] arr)
	{
		if(arr.length == 1)
		{
			return true;
		}
		else
		{
			for(int i=1;i<arr.length;i++)
			{
				if(arr[i] < arr[i-1])
				{
					return false;
				}
			}
			return true;
		}
	}
}