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;
typedef long double ld;
typedef unsigned long long ull;
#define rep(i,a,b) for(ll i=a;i<=b;++i)
#define rrep(i,a,b) for(ll i=a;i>=b;--i)
#define FOR(i,n)  for(ll i=0;i<n;i++)
#define pb push_back
#define mp make_pair
#define PI 3.14159265358979323846
#define fi first
#define se second
#define all(x)  x.begin(),x.end()
#define IOS ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);

const ll mod = 1e9+7;
const ll INF = 1e18;
const ll MAXN = 3001;

void solve() {
    ll n,x; cin>>n>>x;
    ll a[n]; FOR(i,n) cin>>a[i];

    ll last = 0;
    ll vv[n]; memset(vv,0,sizeof(vv));
    for(int i=n-2; i>=last; i--) {
        vv[i] = vv[i+1];
        if(a[i]>a[i+1]) vv[i] = 1;
    }
    ll ct = 0;
    for(int i = last; i<n; i++) {
        if(i>0 && a[i]<=x && a[i]<a[i-1]) {
            cout<<-1<<"\n";
            return;
        }
        if(a[i]>x && vv[i]==1) {
            ct++;
            ll temp = x;
            x = a[i];
            a[i] = temp;
            
        }
    }
    cout<<ct<<"\n";

}

int main() {
	IOS; 
    #ifndef ONLINE_JUDGE
	   freopen("input.txt", "r", stdin);
	    freopen("output.txt", "w", stdout);
    #endif
    
    ll no_of_test_cases; cin>>no_of_test_cases; 
    //ll no_of_test_cases = 1;
	while(no_of_test_cases--) {
      solve();
    } 
    return 0; 
}