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 ll long long 
#define F first
#define S second
#define pb push_back
#define endl "\n";
#define ios ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
const int MAX = 1e5 + 1;
const int MOD = 1e9 + 7;
const int INF = 1e9;
const ll LINF = 1e18;
int get_element(int a[],int n,int x)
{
    for(int i=0;i<n;i++)
    {
        if(a[i]>x) return i;
    }
    return -1;
}
void solve()
{
   int n,x;
   cin>>n>>x;
   int a[MAX];
   for(int i=0;i<n;i++)cin>>a[i];
   int cnt = 0;
   while(!is_sorted(a,a+n))
   {
       int ind = get_element(a,n,x);
       if(ind<0)
       {
           cnt = -1;
           break;
       }
      swap(a[ind],x);
     cnt = cnt + 1; 
   }
   cout<<cnt<<endl;
}
int main()
{
int test;
cin>>test;
while(test--)
{
    solve();
}
	return 0;
}

