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;

const int N = 1e6+10;
int a[N];
int b[N];
int f[N];

void solve()
{
	int n,x;
	scanf("%d%d",&n,&x);
	for(int i=1;i<=n;i++)	scanf("%d",&a[i]),b[i]=a[i];
	int flag=0;
	sort(b+1,b+n+1);
	for(int i=1;i<=n;i++)
	{
		if(a[i]!=b[i])
		{
			flag=1;
			break;
		}
	}
	if(flag==1&&b[n]<=x)
	{
		printf("-1\n");
		return ; 
	}
	else if(flag==0){
		cout<<"0"<<endl;
	}
	else {
		flag=0;
		for(int i=n;i>=1;i--)
		{
			if(a[i]<x) flag=1;
			
		}
		int res=0,flag=0;
		for(int i=1;i<=n;i++)
		{
			flag=0;
			if(a[i]>x)
			{
				
				swap(a[i],x);
				res++;
				for(int i=2;i<=n;i++)
				{	
					if(a[i]<a[i-1])
					{
						flag=1;
						break;
					}
				}
				if(flag==0)
				{
					cout<<res<<endl;
					return ;
				}
			}
		}
		cout<<"-1"<<endl;
	


		
	}
	
	
		
	
}

int main()
{
	int t;
	scanf("%d",&t);
	while(t--)
	{
		solve();
	}
	
}

 
			    	         	 					 			 		