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
// Author : deetav
// Happy stalking ! ^_^
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
using namespace std;
#define endl "\n"

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);cout.tie(nullptr);cerr.tie(nullptr);
    int64_t t=1;
    cin>>t;
    while(t--)
    {
        int n,x;cin>>n>>x;
        vector <int> lol,v;
        for(int i=0,z;i<n;i++){
            cin>>z;
            lol.push_back(z);v.push_back(z);
        }
        sort(lol.begin(),lol.end());
        if(lol==v){
            cout<<0<<endl;continue;
        }
        bool sorted=false;
       for(int i=0;i<n && !is_sorted(v.begin(),v.end());i++){
           for(int ii=0;ii<n;ii++){
               if(v[ii]>x){
                   swap(x,v[ii]);break;
               }
           }
           if(is_sorted(v.begin(),v.end())){
               sorted=true;
               cout<<i+1<<endl;break;
           }
       }
       if(!sorted){
           cout<<-1<<endl;
       }
    }
    return EXIT_SUCCESS;
}