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>
    using namespace std;
    #define pb push_back 
    #define mk make_pair 
    #define ff first 
    #define ss second 
    typedef long long ll;
 
	
    int main(){
		int t;
		cin>>t;
		while(t--){
			int n,x;
			cin>>n>>x;
			int a[n],b[n+1];
			b[0]=x;
			for(int i=0;i<n;i++){
				cin>>a[i];
				b[i+1]=a[i];
				}
			sort(b,b+n+1);
			int l=0,ans=0;
			bool ok=1;
			for(int i=0;i<n;i++){
				if(a[i]!=b[l]&&x!=b[l]){
					ok=0;
					break;
					}
				if(a[i]==b[l]){
					l++;
					continue;
					}
				bool con=1;
				for(int j=i+1;j<n;j++) if(a[j]<a[j-1]) {con=0;break;}
				if(con)break;	
				l++;
				swap(x,a[i]);
				ans++;
						
				}
			if(!ok)cout<<-1<<"\n";	
			else cout<<ans<<"\n";	
			}
	return 0;
	}
