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
// coached by rainboy
import java.io.*;
import java.util.*;

public class CF1455D extends PrintWriter {
	CF1455D() { super(System.out); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF1455D o = new CF1455D(); o.main(); o.flush();
	}

	int[] aa;
	int solve(int n, int x) {
		int ans = 0;
		for (int h = 0, i, j; h < n; h = j + 1) {
			j = h;
			while (j + 1 < n && aa[j] <= aa[j + 1])
				j++;
			if (j + 1 == n)
				break;
			// aa[j] > aa[j + 1]
			if (x > aa[j + 1] || j > h && aa[j - 1] > aa[j + 1])
				return -1;
			i = j;
			while (i > h && aa[i - 1] > x)
				i--;
			ans += j - i + 1;
			while (i < j) {
				if (aa[i] == aa[i + 1])
					ans--;
				i++;
			}
			x = aa[j];
		}
		return ans;
	}
	void main() {
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			int x = sc.nextInt();
			aa = new int[n];
			for (int i = 0; i < n; i++)
				aa[i] = sc.nextInt();
			if (n == 1) {
				println(0);
				continue;
			}
			println(solve(n, x));
		}
	}
}
