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<iostream>
#include<bits/stdc++.h>
#include<vector>
#define vi vector<lli>
#define lli long long int
#define fo(i,n) for(lli i=1;i<=n;i++)
#define foo(i,n) for(lli i=0;i<n;i++)
#define ff first
#define ss second
#define pb push_back
#define vii vector<lli>
#define ok ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
using namespace std;
#define vp vector<pair<lli,lli>>
#include <map> 
#define mod 1000000007

bool not_sorted(vii &v){
	foo(i,v.size()-1){
		if(v[i]>v[i+1]) return true;
	}
	return false;
}

void swapp(lli &a, lli &b){
	lli t = a;
	a=b;
	b=t;
}

void solve(){
	lli n,x; cin>>n>>x;
	vii v(n);
    foo(i,n) cin>>v[i];
	int c=0;
	while(not_sorted(v)){
		int f=0;
		foo(i,v.size()){
			if(v[i]>x){
				swapp(v[i],x);
			    c++;
			    f=1;
			    break;
			}
		}
		if(!f) {
			cout<<"-1\n";
			return;
		}
	}	
	cout<<c<<"\n";
}


int main(){
	int t; cin>>t;
	while(t--){
		solve();
	}
}