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 ll long long
#define ld long double
#define pll pair<long long,long long>
#define vll vector<long long>
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define deb(x) cout << #x << "=" << x << endl
#define F(i,a,b) for(ll i=a;i<=b;i++)
#define RF(i,a,b) for(ll i=a;i>=b;i--)
#define in(a,n) F(i,0,n-1)cin>>a[i]
#define vi vector<int>
#define out(a,n) F(i,0,n-1)cout<<a[i]<<" ";cout<<endl
#define mod 998244353
#define trace1(x)                cerr<<#x<<": "<<x<<endl
#define trace2(x, y)             cerr<<#x<<": "<<x<<" | "<<#y<<": "<<y<<endl
#define trace3(x, y, z)          cerr<<#x<<":" <<x<<" | "<<#y<<": "<<y<<" | "<<#z<<": "<<z<<endl
#define trace4(a, b, c, d)       cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<endl
#define trace5(a, b, c, d, e)    cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<" | "<<#e<< ": "<<e<<endl
#define trace6(a, b, c, d, e, f) cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<" | "<<#e<< ": "<<e<<" | "<<#f<<": "<<f<<endl
//#define int long long
const int N= 5e3+5;

int n,x;
int a[501];
int dp[501][501][501];

int solve(int idx,int val,int lst)
{
   if(idx==n+1)return 0;
   
   int &ans=dp[idx][val][lst];
   if(ans!=-1)return ans;
   
   int ret=1e9;
   if(lst<=a[idx])ret=solve(idx+1,val,a[idx]);
   
   if(val<a[idx] and lst<=val)
   ret=min(ret,1+solve(idx+1,a[idx],val));
    
    
    return ans=ret;
}

void solve()
{   
   // memset(dp,-1,sizeof dp);
        cin>>n>>x;
        for(int i=1;i<=n;i++)for(int j=0;j<=500;j++)for(int k=0;k<=500;k++)dp[i][j][k]=-1;
        for(int i=1;i<=n;i++)cin>>a[i];
   
   
        int ans=solve(1,x,0);
        if(ans>=1e9)ans=-1;
        cout<<ans<<'\n';
        
}


int main()
{
	ios::sync_with_stdio(false);
    cin.tie(NULL);
    
	int t=1;
   cin>>t;
	while(t--)solve();
	    
   
}