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 <bits/stdc++.h>
using namespace std;
#define intt long long int
#define F first
#define S second
//#define fastio ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
//intt MAX = 10000007;
intt M=1000000007;

int main()
{   
   int t;cin>>t;
   while(t--)
   {
       int n,x;cin>>n>>x;
       int arr[n+1];
       arr[0]=-1;
       for(int i=1;i<=n;i++) cin>>arr[i];
       int sr[n+1]; // sorted right;
       sr[n]=1;
       for(int i=n-1;i>=0;i--)
       {
           if(arr[i]<=arr[i+1] && sr[i+1]==1) sr[i]=1;
           else sr[i]=0; 
       }

int cc=0; int ans=0;

       for(int i=1;i<=n ;i++)
       {

           if(sr[i] && arr[i]>=arr[i-1])
           break;
           if(arr[i]<=x)
           {
                if(arr[i]>=arr[i-1]) continue;
                else
                {   
                    cc=1;break;
                }
           }

           swap(x,arr[i]);
          // cout<<i<<endl;
           ans++;
           

       }
       if(cc) cout<<-1<<endl;
       else cout<<ans<<endl;

   }
    return 0;
}