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
// package com.company;

import java.util.Scanner;

public class aaa {
  static   int dp[][];
    public static void main(String[] args) {
        Scanner input=new Scanner(System.in);

        int t=input.nextInt();
        while (t-->0){
            dp=new int[501][501];
            for (int i = 0; i <501 ; i++) {
                for (int j = 0; j <501 ; j++) {
                        dp[i][j]=-1;

                }
            }
            int n=input.nextInt();
            int x=input.nextInt();
            int a[]=new int[n];
            for (int i = 0; i <n ; i++) {
                a[i]=input.nextInt();

            }

            int ans=dfs(0,x,a,0);
            if (ans==inf){
                System.out.println(-1);
            }else {
                System.out.println(ans);
            }

        }

        }
        static int inf= (int) 1e5;

    private static int dfs(int i, int x, int[] a,int prev) {

        if (i>=a.length) return 0;
        int ans=inf;
        if (dp[i][x]!=-1) return dp[i][x];

        //problem
        if (i<a.length-1 && a[i]>a[i+1]){

            //let's see can i solve it
            if (a[i]>x && x<=a[i+1]&&x>=prev ){

                ans=Math.min(ans,1+dfs(i+1, a[i], a,x));
            }else {
                return (int) 1e5;
            }


        }else {
            //swap
            if (a[i]>x && x>=prev){
                ans=Math.min(ans,1+dfs(i+1, a[i], a,x));
            }
            //dont swap
            ans=Math.min(ans,dfs(i+1, x, a,a[i]));
        }

        return dp[i][x]=ans;




    }


}
