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;
//SET PRECIOSION   cout << fixed ;  cout << setprecision(n) << ans << endl;
#define ll long long
#define sz(v) ((int)(v).size())
#define all(v) (v).begin(), (v).end()
#define FAST ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
vector <ll> v;
ll x,y,z,a,b,c,sum,ans,total,t,cnt,n,m,k,p,kase;
string s1,s2;
map<ll,ll> mp;
set<ll> s;
map<ll,ll> :: iterator itr1, ptr1;
set<ll> :: iterator itr, ptr;

int main()
{
    FAST;
    cin>>t;
    while(t--)
    {
        cin>>n>>x;
        v.resize(n);
        for(ll i=0; i<n; i++)
            cin>>v[i];
        if(is_sorted(all(v)))
            cout<<0<<endl;
        else
        {
            ans = 0;
            for(ll j=0; j<n; j++)
            {
                for(ll i=1; i<n; i++)
                {
                        if(x<v[i-1])
                        {
                            swap(x,v[i-1]);
                            ans++;
                            break;
                        }

                }
                if(is_sorted(all(v)))
                    break;

            }
            if(is_sorted(all(v)))
            cout<<ans<<endl;
            else
                cout<<-1<<endl;

        }
    }
    //clear vectors and maps you idiot
    // check array size dumb
    // use long long instead of int too
    return 0;
}

