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
/* loser001 */

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class CodeForces extends Functions {
    public static void main(String[] args) {
        Scanner sc = new Scanner();
        int testCase = sc.nextInt();
//        int testCase = 1;
        while (testCase-->0){
              int n = sc.nextInt();
              int x = sc.nextInt();
              int[] arr = sc.setIntegerArray(n);
              int c = 0;
              while (true){
                  boolean isSorted = true;
                  int max = arr[0];
                  for(int i=1;i<n;i++) {
                      if (arr[i] < arr[i - 1]) {
                          isSorted = false;
                      }
                      max = Math.max(max,arr[i]);
                  }
                  if(isSorted || x>=max)break;
                  for(int i=0;i<n;i++)
                      if(x<arr[i]){
                          int temp = x;
                          x=arr[i];
                          arr[i]=temp;
                          break;
                      }
                  c++;

              }
              boolean isSorted = true;
              for(int i=1;i<n;i++)
                  if(arr[i]<arr[i-1]){
                      isSorted = false;
                      break;
                  }
            if(!isSorted) System.out.println(-1);
            else System.out.println(c);
        }
    }


}

class Scanner {
    private final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private StringTokenizer st = new StringTokenizer("");
    public String next(){
        while (!st.hasMoreTokens())
            try {
                st = new StringTokenizer(br.readLine());
            }
            catch (IOException e){
                e.printStackTrace();
            }
        return st.nextToken();

    }
    public int nextInt(){
        return Integer.parseInt(next());
    }
    public long nextLong(){
        return Long.parseLong(next());
    }
    public double nextDouble(){
        return Double.parseDouble(next());
    }
    public int[] setIntegerArray(int n){
        int[] arr =new int[n];
        for(int i=0;i<n;i++)arr[i] = nextInt();
        return arr;
    }
    public long[] setLongArray(int n){
        long[] arr =new long[n];
        for(int i=0;i<n;i++)arr[i] = nextLong();
        return arr;
    }
    public int[][] setIntegerMatrix(int r,int c){
        int[][] arr = new int[r][c];
        for(int i=0;i<r;i++)
            for(int j=0;j<c;j++)
                arr[i][j]=nextInt();
        return arr;
    }
}
class Functions {
    public static int mod = (int)1e9+7;
    public static void sort(int[] a){
        ArrayList<Integer> temp = new ArrayList<>();
        for (int j : a) temp.add(j);
        Collections.sort(temp);
        for(int i=0;i<a.length;i++)a[i] = temp.get(i);
    }
    public static void sortRev(int[] a){
        sort(a);
        int left = 0;
        int right = a.length-1;
        while (left<right){
            int temp =a[left];
            a[left] = a[right];
            a[right] = temp;
            left++;
            right--;
        }
    }
    public static long factorial(int n){
        long fact = 1L;
        for(int i=2;i<=n;i++)fact=  (fact*i)%mod;
        return fact;
    }

    public static long smallestFactor(long n){
        for(long i=2 ;i*i<=n;i++)
            if(n%i==0)
                return i;
        return -1;
    }
}
/*
 public static void main(String[] args) {
        Scanner sc = new Scanner();
        int testCase = sc.nextInt() ;
        int c=1;
        while (c<=testCase){
            int n = sc.nextInt();
            long k = sc.nextLong();
            int[] arr = sc.setIntegerArray(n);
            Map<Integer , Long> i_k = new HashMap<>(n);
            Map<Long , Boolean> k_ans = new HashMap<>(n);
            long start =System.currentTimeMillis();
            boolean my = find(arr,k,0,i_k,k_ans);
            long end = System.currentTimeMillis();
            boolean corr = findR(arr,k,0);
            long endC = System.currentTimeMillis();
            System.out.println("time took : "+(end-start)/1000.0);
            System.out.println("time took in correct : "+(endC-end)/1000.0);
            System.out.println(my+" "+ corr);
            c++;

        }
    }
    private static boolean findR(int[] arr, long k,int i) {
        if(k==0)return true;
        if(i>=arr.length)return false;
        return findR(arr,k,i+1) || findR(arr,k-arr[i],i+1);
    }
    private static boolean find(int[] arr, long k,int i, Map<Integer , Long> i_k ,Map<Long , Boolean> k_ans ) {
        if(k==0)return true;
        if(k<0)return false;
        if(i==arr.length)return false;
        if(i_k.containsKey(i) && k_ans.containsKey(i_k.get(i)))
            return k_ans.get(i_k.get(i));
        if(!i_k_ans.containsKey(i))
            i_k_ans.put(i,new HashMap<>());
        i_k_ans.get(i).put(k,find(arr,k-arr[i],i+1,i_k_ans) || find(arr,k,i+1,i_k_ans));

        return i_k_ans.get(i).get(k);
    }

 */