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.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        Scanner in = new Main().new Scanner(inputStream);
        Main solver = new Main();
        solver.runn(in);
    }

    long MOD = 1000000007L;

    public void runn(Scanner in) {
        int t = in.ni();
        while (t-- > 0) {
            int n = in.ni(), x = in.ni();
            int[] arr = in.nia(n);
            int id = 0;
            while (unsorted(arr)) {
                int i = 0;
                for (; i < n; i++)
                    if (arr[i] > x)
                        break;
                if (i == n)
                    break;
                int temp = arr[i];
                arr[i] = x;
                x = temp;
                id++;
            }
            if (unsorted(arr))
                System.out.println(-1);
            else
                System.out.println(id);
        }
    }

    public boolean unsorted(int[] arr) {
        for (int i = 0; i < arr.length - 1; i++)
            if (arr[i] > arr[i + 1])
                return true;
        return false;
    }

    class Scanner {
        BufferedReader br;
        StringTokenizer in;

        public Scanner(InputStream inputStream) {
            br = new BufferedReader(new InputStreamReader(inputStream));
        }

        public String next() {
            return hasMoreTokens() ? in.nextToken() : null;
        }

        public String rl() {
            try {
                return br.readLine();
            } catch (Exception e) {
                e.printStackTrace();
                return null;
            }
        }

        boolean hasMoreTokens() {
            while (in == null || !in.hasMoreTokens()) {
                String s = rl();
                if (s == null)
                    return false;
                in = new StringTokenizer(s);
            }
            return true;
        }

        public String nextString() {
            return next();
        }

        public int ni() {
            return Integer.parseInt(nextString());
        }

        public double nd() {
            return Double.parseDouble(nextString());
        }

        public long nl() {
            return Long.parseLong(nextString());
        }

        public int[] nia(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public long[] nla(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

    }

    int stoi(String a) {
        return Integer.parseInt(a);
    }

    void debug(int[] arr) {
        System.out.println(Arrays.toString(arr));
    }

    void debug(int[][] arr) {
        for (int i = 0; i < arr.length; i++) {
            for (int j = 0; j < arr[i].length; j++)
                System.out.print(arr[i][j] + "\t");
            System.out.println();
        }
    }

    class Pair implements Comparable<Pair> {
        int a;
        int b;

        public Pair(int x, int y) {
            a = x;
            b = y;
        }

        public int compareTo(Pair other) {
            if (a == other.a)
                return Integer.compare(b, other.b);
            else
                return Integer.compare(a, other.a);
        }

        public int hashCode() {
            return a * 100007 + b;
        }

        public boolean equals(Object other) {
            Pair o = (Pair) other;
            return a == o.a && b == o.b;
        }
    }
}
