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 static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import java.util.*;
import java.io.*;
import java.math.*;

   public class x1455D
   {
      public static void main(String hi[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int T = Integer.parseInt(st.nextToken());
         StringBuilder sb = new StringBuilder();
         while(T-->0)
         {
            st = new StringTokenizer(infile.readLine());
            int N = Integer.parseInt(st.nextToken());
            int X = Integer.parseInt(st.nextToken());
            int[] arr = new int[N+1];
            st = new StringTokenizer(infile.readLine());
            for(int i=0; i < N; i++)
               arr[i+1] = Integer.parseInt(st.nextToken());
            //compress
            ArrayList<Integer> ls = new ArrayList<Integer>();
            ls.add(X);
            for(int x: arr)
               ls.add(x);
            Collections.sort(ls);
            int boof = 0;
            int[] map = new int[501];
            Arrays.fill(map, -1);
            for(int x: ls)
               if(map[x] == -1)
                  map[x] = boof++;
            for(int i=0; i <= N; i++)
               arr[i] = map[arr[i]];
            X = map[X];
            int MAX = boof;
            int[][][] dp = new int[N+1][MAX+1][MAX+1];
            for(int i=0; i <= N; i++)
               for(int a=0; a <= MAX; a++)
                  Arrays.fill(dp[i][a], 690);
            dp[0][0][X] = 0;
            for(int i=1; i <= N; i++)
            {
               for(int p=0; p <= arr[i]; p++)
                  for(int x=0; x <= MAX; x++)
                     dp[i][arr[i]][x] = min(dp[i][arr[i]][x], dp[i-1][p][x]);
               for(int x=0; x < arr[i]; x++)
                  for(int p=0; p <= x; p++)
                     dp[i][x][arr[i]] = min(dp[i][x][arr[i]], dp[i-1][p][x]+1);
            }
            int res = 690;
            for(int end=0; end <= MAX; end++)
               for(int x=0; x <= MAX; x++)
                  res = min(res, dp[N][end][x]);
            if(res == 690)
               res = -1;
            sb.append(res+"\n");
         }
         System.out.print(sb);
      }
   }