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
//package cp; 
import java.util.*;
import java.io.*;

public class Solution
{ 
	static int sorted(int arr[], int n)
    {
        if (n == 1 || n == 0)
            return 1;
        if (arr[n - 1] < arr[n - 2])
            return 0;
        return sorted(arr, n - 1);
    }
	public static void main(String[] args)  
	{ 
		FastScanner sc = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		int t=sc.nextInt();
		while(t-- >0) {
			int n=sc.nextInt(),x=sc.nextInt();
			int a[]=sc.readArray(n);
			int count=0;boolean flag=false;
			for(int i=0 ; i<n ; i++) {
				if(sorted(a,n)!=0) {
//					out.println(count);
					flag=true;
					break;
				}
				if(a[i] > x) {
					int temp=x;
					x=a[i];
					a[i]=temp;
					count++;
				}
			}
			if(flag==true) {
				out.println(count);
			}
			else {
				out.println(-1);
			}
		}
		out.flush();
		out.close();
	}
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int [] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
} 
class MyComparator implements Comparator<Pair> {
	public int compare(Pair a, Pair b) {
		return (int)a.first - (int)b.first;
	}
}

class Pair {
	long first;
	long second;
}

