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 D {

	public static void main(String[] args) {
		
		Scanner s = new Scanner(System.in);
		int t = s.nextInt();
		for (int z = 0; z < t; z++) {
			
			int n = s.nextInt();
			int x = s.nextInt();
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = s.nextInt();
			}
			int moves = 0;
			while (!sorted(arr)) {
				boolean placed = false;
				for (int i = 0; i < n; i++) {
					if (arr[i] > x) {
						int tmp = arr[i];
						arr[i] = x;
						x = tmp;
						placed = true;
						moves++;
						break;
					}
				}
				if (!placed) {
					break;
				}
			}
			if (sorted(arr)) {
				System.out.println(moves);
			} else {
				System.out.println(-1);
			}
			
		}
		
	}
	
	public static boolean sorted(int[] arr) {
		for (int i = 1; i < arr.length; i++) {
			if (arr[i] < arr[i - 1]) {
				return false;
			}
		}
		return true;
	}
	
}
