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 <algorithm>
#include <vector>
using namespace std;
int n,a[510],x0;
bool sp[510];
void solve() {
	cin >> n >> x0;
	vector<int> sps;
	for (int i = 1; i <= n; i++) cin >> a[i], sp[i] = false;
	for (int i = 2; i <= n; i++) {
		
		int t = 0;
		for (int j = 1; j < i; j++) if (a[j] > a[i])t++;
		if (t > 1) { cout << -1 << endl; return; }
	}
	int res = 0;
	for (int i = 1; i < n; i++) {
		if (a[i] > a[i + 1]) sp[i] = true,res++, sps.push_back(i);
	}
	int x = x0;
	if (res == 0) { cout << 0 << endl; return; }
	

	if (x > a[sps[0] + 1]) {
		cout << -1 << endl; return;
	}
	int st = 1;
	for (int i = 0; i < sps.size(); i++) {
		
		for (int j = st; j < sps[i]; j++) {
			if (a[j] > x) {
				int temp = a[j];
				a[j] = x; x = temp;
				res++;
			}
		}
		int temp = a[sps[i]];
		a[sps[i]] = x; x = temp;
		st = sps[i] + 1;
	}
	
	cout << res << endl;
}
int main()
{
	int t; cin >> t;
	while (t--) solve();
//	system("pause");
    return 0;
}

