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 END '\n'
#define ll long long
#define pb push_back
#define pii pair<int, int>
#define ff first
#define ss second
#define bug(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
#define loop(i, a, b) for(int i = (a); i < (b); i++)
#define loopb(i, b, a) for(int i = (b); i > (a); --i) 
const ll inf = 1e18;  
const int mod = 1e9+7;
const int mod1 = 998244353;
const int nax = 505;
int n,x,a[nax],dp[nax][nax];
int calc(int pos, int X)
 {
  if(pos == n)
     return 0;
  if(dp[pos][X] == -1)
     {
      int now = n + 1;
      if(a[pos] <= a[pos + 1])
         now = min(now, calc(pos + 1, X));
      if(a[pos] > X && (pos == 0 || a[pos - 1] <= X) && X <= a[pos + 1])
         {
          swap(a[pos], X);
          now = min(now, calc(pos + 1, X) + 1);
          swap(a[pos], X);
         }
      dp[pos][X] = now; 
     }
  return dp[pos][X];
 }
void solve()
 {
  cin>>n>>x;
  loop(i,0,n)
   cin>>a[i];
  a[n] = a[n - 1] + 1;
  loop(i,0,n + 1)
   loop(j,0,501)
    dp[i][j] = -1;
  int ans = calc(0,x);
  if(ans == n + 1)
     ans = -1;
  cout<<ans<<END;
 } 
int32_t main()
 {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0); 
  #ifndef ONLINE_JUDGE
   freopen("input.txt","r",stdin);
   freopen("output.txt","w",stdout);
   freopen("error.txt","w",stderr);
  #endif
   int t;
   cin>>t;
   while(t--)
     solve();
 // cerr<<END<<1.0*clock()/CLOCKS_PER_SEC;
  return 0;
} 