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 = 505;
int n, k, maxx[N][N], a[N], pv[N], b[N];
bool issorted(int b[])
{
    int f = 1;
    for (int i = 1; i < n; ++i)
    {
        f = f && b[i] >= b[i - 1];
    }
    return f;
}
void solve()
{
    cin >> n >> k;
    for (int i = 0; i < n; ++i)
    {
        pv[i] = -1;
        cin >> a[i];
    }
    if (issorted(a))
    {
        cout << 0 << '\n';
        return;
    }
    for (int i = 0; i < n; ++i)
    {
        int x = -1;
        for (int j = i; j < n; ++j)
        {
            x = max(x, a[j]);
            maxx[i][j] = x;
        }
    }
    for (int i = 0; i < n; ++i)
    {
        for (int j = i - 1; j >= 0; --j)
        {
            if (j == i - 1 && a[j] > k && a[j] < a[i])
                pv[i] = j;
            else
            {
                if (maxx[j + 1][i - 1] <= a[j] && a[j] > k && a[j] < a[i])
                    pv[i] = j;
            }
        }
    }
    
    int ans = -1;
    for (int i = n - 1; i >= 0; --i)
    {



        for (int j = 0; j < n; ++j)
            b[j] = a[j];




        if (pv[i] == -1)
        {
            if (a[i] > k)
                b[i] = k;
            if (issorted(b))
            {
                if (ans == -1)
                    ans = 1;
                else
                    ans = min(ans, 1);
            }
            continue;
        }



        int  l = 0, idx = i;
        
        while (pv[idx] != -1)
        {
            b[idx] = a[pv[idx]];
            idx = pv[idx];
            l ++;
        }
        b[idx] = k;
        l ++;
        if (issorted(b))
        {
            
            if (ans == -1)
                ans = l;
            else
                ans = min(ans, l);
        }
    }
    cout << ans << '\n';
}
int main(int argc, char const *argv[])
{
    int t;
    cin >> t;
    while (t --)
        solve();
    return 0;
}