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 <vector>
#include <algorithm>
#include <sstream>
#include <fstream>
#include <queue>
#include <deque>
#include <bitset>
#include <iterator>
#include <list>
#include <stack>
#include <map>
#include <set>
#include <functional>
#include <numeric>
#include <utility>
#include <limits>
#include <time.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <assert.h>

#define ll long long


using namespace std;

#define PI 3.14159265

const int modval = 10e9+7;

int main(){
    int t;
    cin>>t;
    for(int i = 0; i < t; i++){
        int n;
        cin>>n;
        int x;
        cin>>x;
        vector<int> h;
        for(int j = 0; j < n; j++){
            int val;
            cin>>val;
            h.push_back(val);
        }

        if(is_sorted(h.begin(), h.end())){
            cout<<0<<endl;
            continue;
        }
        int count = 0;
        for(int j = 0; j < n; j++){
            if(h[j] > x){
                swap(h[j], x);
                count++;

                if(is_sorted(h.begin(), h.end())){
                    break;
                }
            }
        }
        if(is_sorted(h.begin(), h.end())){
            cout<<count<<endl;
        }else{
            cout<<-1<<endl;
        }


    }

    return 0;
}
