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
#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<unordered_map>
#include<cmath>
#include<queue>
using namespace std;
// #define size 20001

#define ll long long int

bool checkSorted(int arr[] , int n)
{
    for(int i=0; i<n-1; ++i)
        if( arr[i] > arr[i+1] )
            return false;
            
    return true;
}

int main()
{
    int t;
    cin>>t;
    while(t--)
    {
        int n,x,arr[500];
        cin>>n>>x;
        for(int i=0; i<n; ++i)
            cin>>arr[i];
        
        if(checkSorted(arr,n))
        {
                cout<<0<<endl;
                continue; 
        }
        
        int swap=0;
        while(swap < n && checkSorted(arr,n) == false)
        {
            bool swapped=false;
            for(int i=0; i<n; ++i)
            {
                if(arr[i] > x)
                {
                    int temp=arr[i];
                    arr[i]=x;
                    x=temp;
                    ++swap;
                    swapped=true;
                    break;
                }
            }
            
            if(swapped==false && checkSorted(arr,n)==false)
            {
                swap=-1;
                break;
            }
        }
        if(swap == n)
            swap=-1;
        
        cout<<swap<<endl;
    }
}











