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 int
#define P 1000000007
#define inf 1e18

ll get_first(vector<ll> &v, ll x)
{
    ll i;
    for (i = 0; i < v.size(); i++)
    {
        if (v[i] > x)
            return i;
    }
    return -1;
}

int main()
{
    ll i, t;
    cin >> t;
    while (t--)
    {
        ll n, x;
        cin >> n >> x;
        vector<ll> a(n);
        for (i = 0; i < n; i++)
            cin >> a[i];
        ll ans = 0;

        while (!is_sorted(a.begin(), a.end()))
        {
            ll index = get_first(a, x);
            if (index < 0)
                break;
            swap(a[index], x);
            ans++;
        }

        if (is_sorted(a.begin(), a.end()))
            cout << ans << "\n";
        else
            cout << "-1\n";
    }

    return (0);
}
