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;
typedef long long LL;
const int N = 500+5;
const int inf = 1e5+5;


int main(){
    ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);

    int tc;
    cin>>tc;
    while(tc--){
        int n,x;
        cin>>n>>x;
        vector<int>v(n);
        for(int &x : v) cin>>x;
        vector<int>v2 = v;
        sort(v2.begin(), v2.end());
        if(v==v2) cout<<"0\n";
        else{
            int ans = 0;
            reverse(v.begin(), v.end());
            bool mara = false;
            while(v.size()>=2){
                vector<int>tmp={x};
                while(v.size()>=2 and v.back()<=v[v.size()-2] and v.back()<=x) v.pop_back();
                while(v.size()>=2 and v.back()<=v[v.size()-2]) {
                    if(v.back()>tmp.back())
                        tmp.push_back(v.back());
                    v.pop_back();
                }
                if(v.size()>=2 and v.back()>v[v.size()-2]){
                    if(v[v.size()-2]>=tmp.back()){
                        ans += tmp.size();
                        x = v.back();
                        v.pop_back();
                    }
                    else {
                        mara = true;
                        break;
                    }
                }
            }
            if(mara) cout<<"-1\n";
            else cout<<ans<<"\n";
        }
    }

}
/*
1
10 6
8 5 6 7 8 9 10 11 12 14
*/
