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
//////////////////////////// ****   JAI SHREE RAM   **** //////////////////////////
#include<bits/stdc++.h>
#include<unordered_map>
using namespace std;
#define int long long int
#define double long double
void fun() {
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);freopen("output.txt", "w", stdout);
   #endif
}
int __gcd(int a, int b) {if(b==0) return a; return __gcd(b, a%b);}
int poww(int a, int b, int md) {if(b<0) return 0; if(a==0) return 0; int res=1;
    while(b) {if(b&1){res=(1ll*res*a)%md;}a=(1ll*a*a)%md;b>>=1;}return res;}
int divide(int a, int b, int md) {int rr=a*(poww(b, md-2, md));rr%=md;return rr;}
//////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////
const int size = 1e5 + 5;
//////////////////////////////////////////////////////////////////////////////////
signed main() {
    ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); fun();
    int t; cin >> t;
    while(t--) {
    	int n, x; cin >> n >> x;
    	int arr[n + 1];
    	for(int i = 1; i <= n; i++) {
    		cin >> arr[i];
    	}
    	bool flag = true;
    	int ans = 0;
    	for(int i = 1; i < n; i++) {
    		bool isSorted = true;
    		for(int j = i + 1; j <= n; j++) {
    			isSorted &= arr[j] >= arr[j - 1];
    		}
    		if(isSorted) {
    			break;
    		} else {
    			if(arr[i] > x) {
    				if(arr[i + 1] >= x) {
    					swap(arr[i], x);
    					ans++;
    				} else {
    					flag = false;
    					break;
    				}
    			} else {
    				if(arr[i + 1] < arr[i]) {
    					flag = false;
    					break;
    				}
    			}
    		}
    	}
    	if(flag) cout << ans << '\n';
    	else cout << "-1\n";
    }
    return 0;
}
























