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.io.PrintWriter;
import java.util.Arrays;
 
public class Main {
    static int T, n, x, ans, b;
    
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int _ = Integer.parseInt(in.readLine());
        while (_-- > 0) {
            String[] s = in.readLine().split(" ");
            int n = Integer.parseInt(s[0]);
            int x = Integer.parseInt(s[1]);
            int[] a = Arrays.stream(in.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
            
            // 直接从前往后扫，遇到 ai>x 就交换，处理到最后一个乱序的位置。
            // 最后若仍然无序则无解。
            
            // 最后一个乱序的位置
            int b = 0;
            for (int i = n - 1; i > 0; i--) {
                if (a[i] < a[i - 1]) {
                    b = i;
                    break;
                }
            }
            
            int ans = 0;
            if (b > 0) {
                for (int i = 0; i <= b; i++) {
                    if (x < a[i]) {
                        int temp = a[i];
                        a[i] = x;
                        x = temp;
                        ans++;
                    }
                }
                for (int i = 1; i < n; i++) {
                    if (a[i] < a[i - 1]) {
                        ans = -1;
                        break;
                    }
                }
            }
            out.println(ans);
        }
        
        out.close();
    }
    
}