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 fast  ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
#define int long long
int32_t main(){
    fast;
    int t;
    cin>>t;
    while(t--){
        int n,x;
        cin>>n>>x;
        int a[n];
        int fl=1;
        for(int i=0;i<n;i++){
            cin>>a[i];
            if(i){
                if(a[i]<a[i-1])
                    fl=0;
            }
        }
        if(fl){
            cout<<0<<"\n";
            continue;
        }
        
        int cnt=0;
        while(1){
            int h=1;
            for(int i=0;i<n;i++){
                if(i){
                    if(a[i]<a[i-1]){
                        h=0;
                        break;
                    }
                }
            }
            if(h==1){
                break;
            }
            int y=-1;
            for(int i=0;i<n;i++){
                if(a[i]>x){
                    y=i;
                    break;
                }
            }


            if(y==-1){
                break;
            }
            swap(a[y],x);
            // for(int i=0;i<n;i++){
            //     cout<<a[i]<<" ";
            // }
            // cout<<y<<"\n";
            cnt++;
        }
        int h=1;
        for(int i=0;i<n;i++){
            if(i){
                if(a[i]<a[i-1])
                    h=0;
            }
        }
        if(h==1){
            cout<<cnt;
        }
        else{
            cout<<-1;
        }


        cout<<"\n";
    }
    



    



}
