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 <cmath>
#include <cstdio>
#include <set>
#include <map>
#include <string>
#include <vector>


//#include <bits/stdc++.h>

using namespace std;

#define INF 1000000007
#define PB push_back
#define MP make_pair
#define X first
#define Y second
#define LB lower_bound
#define UB upper_bound
#define all(v) v.begin(),v.end()

using pii=pair<int,int>;
using vi=vector<int>;
using vii=vector<pii>;
using ll=long long;
using pll=pair<ll,ll>;

void setIO(string s){
  ios_base::sync_with_stdio(0); cin.tie(0);
  freopen((s+".in").c_str(),"r",stdin);
  freopen((s+".out").c_str(),"w",stdout);
}

int main() {
  //setIO("standingout");

	int n;
	int x;
	int testcases;
	cin >> testcases;
	while(testcases--){
		cin >> n >> x;
		int cnt = 0;
		int arr[n];
		for(int i = 0; i < n; i++){
			cin>> arr[i];
		}

		int sortfrombackptr = n-1;
		for(int i = n-1; i>0; i--){
			if(arr[i] >= arr[i-1]){
				sortfrombackptr--;
			}
			else{break;}
		}

		if(sortfrombackptr == 0) cout << 0 << endl;
		else{
			for(int i = 0; i < n; i++){
				if(i == sortfrombackptr-1){
					if(arr[i] <= arr[i+1]){
						break;
					}
					else if(arr[i] > x){
						int temp = x;
						x = arr[i];
						arr[i] = temp;
						cnt++;
						sortfrombackptr++;;
					}
					else{
						break;
					}
				}
				else if(arr[i] > x){
					int temp = x;
					x = arr[i];
					arr[i] = temp;
					cnt++;
				}
			}
			bool tf = true;
			for(int i = 0; tf && i < n-1; i++){
				if(arr[i] > arr[i+1]) tf = false;
			}
			if(!tf) cout <<  -1 << endl;
			else cout << cnt << endl;
		}
	}
//yhing

return 0;
}
