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.Arrays;
import java.util.StringTokenizer;

public class SequenceAndSwaps{
    static boolean check(int[]array){
        int[] cpy = Arrays.copyOf(array, array.length);
        Arrays.sort(cpy);
        for(int i = 0; i < array.length; i ++)
            if(array[i] != cpy[i])
                return false;

        return true;
    }
    public static void main(String[] args) throws IOException{
        BufferedReader r = new BufferedReader(new InputStreamReader(System.in));
        int t1 = Integer.parseInt(r.readLine());
        while(t1 -- > 0){
            StringTokenizer t = new StringTokenizer(r.readLine());
            int n = Integer.parseInt(t.nextToken());
            int x = Integer.parseInt(t.nextToken());
            int[]array = new int[n];
            t = new StringTokenizer(r.readLine());
            for(int i = 0; i < n; i++)
                array[i] = Integer.parseInt(t.nextToken());

            if(check(array)){
                System.out.println(0);
                continue;
            }

            int count = 0;
            for(int i = 0; i < n; i++)
                if(array[i] > x){
                    int temp = x;
                    x = array[i];
                    array[i] = temp;
                    count ++;
                    if(check(array))
                        break;
                }  
            if(!check(array))
                System.out.println(-1);
            else
                System.out.println(count);

        }
    }
    
}