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 fast() ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define li long int
#define pb push_back
#define mp make_pair
#define lb lower_bound
#define ub upper_bound
#define mem(arr,x) memset(arr,x,sizeof(arr))
#define F first
#define S second
#define MOD 1000000007
#define pii pair<lli,lli>
#define lli long long int
const int N=1002;

class cmp{
public:
   bool operator()(const pii &a,const pii &b){
        if(a.S!=b.S) return a.S>b.S;
        return a.F>b.F;
   }
};
void solve(){
    int n,x;
    cin>>n>>x;
    int a[n],i;
    for(i=0;i<n;i++) cin>>a[i];
    int ans=0,f=0;
    for(i=0;i<n;i++){
         if(is_sorted(a,a+n)){
            cout<<ans<<endl;
            return;
         }
         // if(i>0&&a[i]<a[i-1]){
              if(a[i]>x){
                 swap(a[i],x);
                 ans++;
              }
         //      else {
         //          f=1;
         //          break;
         //      }
         // }
    }
    if(f==0&&is_sorted(a,a+n)) cout<<ans<<endl;
    else cout<<"-1"<<endl;
}
int main() {
  #ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
  #endif
        fast();
  int t=1;
  cin>>t;
  while(t--){
    solve();
  }
  return 0;
}