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.*;

public class Main {

	public static void main(String[] args) {
		FastReader reader = new FastReader();
		int t = reader.nextInt();
		while (t-- > 0){
			int n = reader.nextInt();
			int x = reader.nextInt();
			int[] array = new int[n];
			for (int i = 0; i < n; i++){
				array[i] = reader.nextInt();
			}
			int count = 0;
			while (!sorted(array)) {
				int con = 0;
				for (int j = 0; j < n; j++) {
					if (array[j] > x){
						int temp = x;
						x = array[j];
						array[j] = temp;
						count++;
						break;
					}
					else {
						con++;
					}
					if (con == n - 1){
						count = n + 1;
						break;
					}
				}
				if (count > n){
					break;
				}
			}
			if (count > n){
				System.out.println(-1);
			}
			else {
				System.out.println(count);
			}
		}
	}

	static boolean sorted(int[] array){
		boolean sorted = true;
		for (int i = 0; i < array.length - 1; i++){
			if (array[i] > array[i + 1]){
				sorted = false;
				break;
			}
		}
		return sorted;
	}

}

class FastReader {
	BufferedReader br;
	StringTokenizer st;

	public FastReader() {
		br = new BufferedReader(new
				InputStreamReader(System.in));
	}

	String next() {
		while (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}

	int nextInt() {
		return Integer.parseInt(next());
	}

	long nextLong() {
		return Long.parseLong(next());
	}

	double nextDouble() {
		return Double.parseDouble(next());
	}

	String nextLine() {
		String str = "";
		try {
			str = br.readLine();
		} catch (IOException e) {
			e.printStackTrace();
		}
		return str;
	}
}