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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

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

	public static void main(String[] args) throws IOException {
		BufferedReader sc = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(sc.readLine());
		while (--t >= 0) {
			StringTokenizer st = new StringTokenizer(sc.readLine());
			int n = Integer.parseInt(st.nextToken()), x = Integer.parseInt(st.nextToken()), arr[] = new int[n], ans = 0,
					i = 0, flag = 0;
			st = new StringTokenizer(sc.readLine());
			for (int j = 0; j < n; j++)
				arr[j] = Integer.parseInt(st.nextToken());
			while (!sorted(arr)) {
				while (i < n) {
					if (arr[i] > x)
						break;
					++i;
				}
				if (i >= n) {
					System.out.println(-1);
					flag = 1;
					break;
				}
				int temp = arr[i];
				arr[i] = x;
				x = temp;
				++ans;
			}
			if (flag == 0)
				System.out.println(ans);
		}
	}
}
