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
using namespace std;
#include <iostream>
#include <utility>
#include <algorithm>
#define pii pair<int,int>

void Swap (pii &a,pii &b){
    pii t = a;
    a = b;
    b = t;
}

pii x,seq[510],sorted[510];

bool isSorted(int n){
    seq[0].first = -1;
    for (int i=1;i<=n;++i){
        if (seq[i-1].first > seq[i].first){
            return false;
        }
    }
    return true;
}

int main(){
    ios_base::sync_with_stdio(false),cin.tie(0);
    int t;

    cin >> t;
    while (t--){
        int n;

        cin >> n >> x.first;
        sorted[n+1] = {x.first,n+1};
        for (int i=1;i<=n;++i){
            cin >> seq[i].first;
            sorted[i].first = seq[i].first;
            sorted[i].second = i;
        }

        sort (sorted+1,sorted+2+n,[](pii a,pii b){
            return (a.first == b.first ? a.second < b.second : a.first < b.first);
        });

        for (int i=1;i<=n+1;++i){
            seq[sorted[i].second].second = i;
        }
        x.second = seq[n+1].second;

        if (x.second == n+1){
            cout << (isSorted(n) ? 0 : -1) << '\n';
            continue;
        }

        int cnt = 0;
        while (x.second != n+1 && !isSorted(n)){
            if (seq[x.second].first < x.first){
                cnt = -1;
                break;
            }
            else if (seq[x.second].first == x.first){
                Swap (x,seq[x.second]);
            }
            else{
                Swap (x,seq[x.second]);
                ++cnt;
            }
        }

        cout << (isSorted(n) ? cnt : -1) << '\n';
    }

    return 0;
}