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>
#include <chrono> 
using namespace std;
using namespace chrono;
#define aarya ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
#define int long long
const unsigned int M = 1000000007;
int32_t main(){
	auto start = high_resolution_clock::now();
	aarya;
	int t;
	cin>>t;
	while(t--){
		int n,x;
		cin>>n>>x;
		vector<int> v(n);
		int ans=0;
		for(int i=0;i<n;i++)
			cin>>v[i];
		if(is_sorted(v.begin(),v.end()))
			cout<<ans<<endl;
		else{
			while(!is_sorted(v.begin(),v.end())){
				int i;
				for(i=0;i<n;i++){
					if(v[i] > x){
						ans++;
						swap(v[i],x);
						break;
					}
				}
				if(i==n) break;
			}
			if(is_sorted(v.begin(),v.end())) cout<<ans<<endl;
			else cout<<-1<<endl;
		}

	}
	auto stop = high_resolution_clock::now();
    auto duration = duration_cast<microseconds>(stop - start);
    float count = duration.count();
    count /= 1000000;
    //cout << "Time taken by function: "<< count << " seconds" << endl;
    return 0;
}