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
//Comment any cerr statments before submission as it makes the program slow

#include <bits/stdc++.h>
using namespace std;

#define PI 3.14159265358979323846
typedef long long ll;

typedef vector<vector<int>> vec_2i;
typedef vector<vector<bool>> vec_2b;
typedef vector<vector<char>> vec_2c;
typedef vector<int> vec_i;
typedef vector<bool> vec_b;


int main()
{
#ifndef ONLINE_JUDGE
	//for getting input from input text
	freopen("input.txt", "r", stdin);
	//for writing output to output.txt
	freopen("output.txt", "w", stdout);
#endif
	ios_base::sync_with_stdio(false); 
    cin.tie(NULL);
    int t; cin >> t;
    while(t--)
    {
    	int n, x;
    	cin >> n >> x;
    	vector<int> vec(n);
    	for(int i{}; i < n; i++)
    	{
    		cin >> vec[i];
    	}
    	bool sorted{true};
    	int issue{};
    	vector<bool> marked(n);
    	for(int i{}; i < n - 1; i++)
    	{
    		if(vec[i] > vec[i + 1])
    		{
    			sorted = false;
    			marked[i] = true;
    			issue++;
    		}
    	}
    	if(sorted)
    		cout << 0 << '\n';
    	else
    	{
    		int count{};
    		for(int i{}; i < n; i++)
    		{
    			if(vec[i] > x)
    			{
    				int temp{vec[i]};
    				vec[i] = x;
    				x = temp;
    				count++;
    				if(marked[i])
    					issue--;
    				// cerr << count;
    			}
    			if(!issue)
    				break;
    		}
    		sorted = true;
    		for(int i{}; i < n - 1; i++)
    		{
    			if(vec[i] > vec[i + 1])
    				sorted = false;
    		}
    		if(!sorted)
    			cout << -1 << '\n';
    		else
    			cout << count << '\n';

    	}

    }
    return 0;
}
