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
/// HuDzG
#include <bits/stdc++.h>
#define reset(a) memset(a,0,sizeof(a))
#define ll long long
#define ld long double
#define endl '\n'
#define AutoAC int main()
#define OO 1000000000000000000
#define F first
#define S second
#define pii pair <ll, ll>
#define pb push_back
#define nmax 100005
#define HUNGIT "C"
#define MOD 1000000007

using namespace std;

ll n, a[nmax], t, x;

bool check()
{
    for(int i = 1; i <= n; i++)
        if(a[i] < a[i - 1])
        {
            return 0;
        }
    return 1;
}

AutoAC
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
//    freopen (HUNGIT".inp", "r", stdin);
//    freopen (HUNGIT".out", "w", stdout);
    cin >> t;
    while(t--)
    {
        cin >> n >> x;
        for(int i = 1; i <= n; i++)
            cin >> a[i];
        ll res = 0;
        if(check())
        {
            cout << 0 << endl;
            continue;
        }
        for(int i = 1; i <= n; i++)
            if(a[i] > x)
            {
                res++;
                swap(a[i], x);
                if(check()) break;
            }
        for(int i = 1; i <= n; i++)
            if(a[i] < a[i - 1])
            {
                res = -1;
                break;
            }
        cout << res << endl;
    }
    return 0;
}
