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
//LIBRARIES
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <fstream>
#include <cmath>
#include <algorithm>
#include <string>
#include <cstring>
#include <vector>
#include <set>
#include <unordered_set>
#include <map>
#include <unordered_map>
#include <stack>
#include <queue>
#include <deque>
#include <bitset>
#include <chrono>
#include <functional>
//MACROS
#define _crt_secure_no_warnings
#define FREEELO ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define pb push_back
#define mp make_pair
#define INF 0x3F3F3F3F3F3F3F3FLL
#define MAX 200001
#define MAXLL 1000000000000000000LL
#define MOD 1000000007
#define LOGMAX 21
#define ALPHABET 128
#define loop(i, n) for (int i = 1; i <= (n); i++)
#define loop0(i, n) for (int i = 0; i < (n); i++)
#define sz(x) (int)x.size()
#define all(v) v.begin(), v.end()
#define all1(v) v.begin() + 1, v.end()
#define F first
#define S second
#define EPS 1e-6
using namespace std;
//TYPE DEFINITIONS
typedef long long ll;
typedef unsigned long long ull;
typedef long double lld;
typedef pair<ll, ll> llll;
typedef pair<int, int> ii;
typedef unordered_map<int, int> umii;
typedef unordered_map<ll, ll> umll;
typedef unordered_set<int> usi;
typedef unordered_multiset<int> usmi;
//main exec


bool sorted(vector<int> &a){
    bool isSorted = true;
    for (int i = 1; i < sz(a); i++){
        if (a[i] < a[i - 1]) { isSorted = false; break; } 
    }
    return isSorted;
}

int main(){
    FREEELO
    int t; cin >> t;
    while(t--){
        int n; cin >> n; int x; cin >> x;
        vector<int> a(n + 1, -1);
        loop(i, n) cin >> a[i];
        int cnt = 0;
        for (int i = 1; i <= n; i++){
            if (!sorted(a)){
                if (a[i] > x) swap(a[i], x), cnt++;
            }
        }
        if (!sorted(a)) cnt = -1;
        cout << cnt << endl;
    }
}