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>
#define ll long long
#define pp push_back
#define ff first
#define ss second

using namespace std;

ll w,m,nn,mm,ma,mb,h,r,l,ii,jj,x[1000001],y[1000001],z,g,aa,bb,a,b,c,d,vis,k,mod=998244353,q,inf=1e12;
ll T,i,j,n;
vector <ll> v,vv;
vector <ll> vvv;
queue <pair <ll,ll> > qq;
pair <ll,ll> p;
map <ll,ll> mp,mpp,mppp;
set <ll> se,see;
set <pair<ll,ll> > :: iterator it,itt;
string s,s1,t,t1,tt;
char cc[1000001];

int main()
{
    ios::sync_with_stdio(0);
    cin >> T;
    while(T--)
    {
        cin >> n >> k;
        m=k;
        for(i=0;i<n;i++)
        {
            cin >> x[i];
            m=max(x[i],m);
        }
        z=0;
        b=0;
        for(i=1;i<n;i++)
        {
            if(x[i]<x[i-1])
                b=1;
        }
        while(b && k<m)
        {
            b=0;
            z++;
            for(i=0;i<n;i++)
            {
                if(x[i]>k)
                {
                    swap(k,x[i]);
                    break;
                }
            }
            for(i=1;i<n;i++)
            {
                if(x[i]<x[i-1])
                    b=1;
            }
        }
        if(b==0)
            cout << z;
        else
            cout << -1;
        cout << endl;
    }
    return 0;
}
