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.*;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {
//        br = new BufferedReader(new FileReader(new File("subtract.in")));
//        out = new PrintWriter(new File("subtract.out"));
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        int PUTEN = nextInt();
        for (int POMOGI = 0; POMOGI < PUTEN; POMOGI++) {
            int n = nextInt();
            int x = nextInt();
            int[] a = new int[n];
            int []was = new int[n];
            for (int i = 0; i < n; i++){
                a[i] = nextInt();
                was[i] = a[i];
            }
            boolean sorted = true;
            for (int i = 0; i < n - 1; i++) {
                if (a[i] > a[i + 1]) sorted = false;
            }
            if (sorted) {
                out.println(0);
                continue;
            }
            int l = 0;
            int r = 0;
            boolean popka = true;
            while (l != n) {
                while (r + 1 != n && a[r] <= a[r + 1]) r++;
                if(r  + 1== n)break;
                for (int i = l; i <= r; i++) {
                    if (a[i] > x) {
                        for (int j = i; j <= r; j++) {
                            int p = x;
                            x = a[j];
                            a[j] = p;
                        }
                        break;
                    }
                }
                r++;
                l = r;
            }
            int ans = 0;
            for (int i = 0; i < n - 1; i++) {
                if (a[i] > a[i + 1]) popka = false;
                if(was[i] != a[i])ans ++;
            }
            if (popka) out.println(ans);
            else out.println(-1);
        }
        out.close();
    }

    static BufferedReader br;
    static PrintWriter out;
    static StringTokenizer in = new StringTokenizer("");

    static String next() throws IOException {
        while (!in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

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

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

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

}
