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;

long long n,d,a[569];

int main()
{
	long long t,rr,i,j,z;
	
	scanf("%lld",&t);
	for(rr=0;rr<t;rr++)
	{
		scanf("%lld%lld",&n,&d);
		for(i=1;i<=n;i++)
		{
			scanf("%lld",a+i);
		}
		z=0;
		for(i=1;i<=n;i++)
		{
			for(j=i+1;j<=n;j++)
			{
				if(a[j]<a[j-1])
				{
					j=-1;
					break;
				}
			}
			if(j!=-1)
			{
				break;
			}
			if(a[i]>d)
			{
				z++;
				swap(a[i],d);
			}
		}
		for(i=2;i<=n;i++)
		{
			if(a[i]<a[i-1])
			{
				i=-1;
				break;
			}
		}
		if(i==-1)
		{
			z=-1;
		}
		printf("%lld\n",z);
	}
}
