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 unsigned long long ull;
typedef long long ll;
typedef pair<ll, ll> P;
typedef vector<ll> V;
typedef vector<bool> VB;
typedef vector<string> VS;
typedef vector<P> VP;
typedef vector<V> VV;
typedef map<ll, ll> MP;
typedef multimap<ll, ll> MMP;
typedef set<ll> SET;
typedef multiset<ll> MSET;

#define loop(i,n) for(ll i = 0; i < n; i++)
#define loopr(i,x,y) for(ll i = x; i < y; i++)
#define pb push_back
#define mp make_pair
#define F first
#define S second
#define all(x) (x).begin(), (x).end()
#define clr(x) memset(x, 0, sizeof(x))
#define sortall(x) sort(all(x))
#define deb(x) cout << #x << "=" << x << endl
#define endl '\n'
#define PI 3.1415926535897932384626
#define MOD 1000000007

int main() {

	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);

	ll test;

	cin >> test;

	while (test--) {

		int n, x;

		cin >> n >> x;

		int a[n];

		loop (i, n) {
			cin >> a[i];
		}

		bool poss = true;

		bool found = false;

		int ind = -1;

		loop (i, n) {

			if (a[i] > x) {
				found = true;
				ind = i;
			}

			if (found && a[i] < x) {
				poss = false;
				break;
			}
		}

		int ans = 0;

		if (poss) {

			if (ind == -1) {

				for (int i = 0; i < n - 1; i++) {

					if (a[i + 1] < a[i]) {
						poss = false;
						break;
					}
				}
			} else {

				bool req = false;

				for (int i = 0; i < n - 1; i++) {

					if (a[i + 1] < a[i]) {
						req = true;
						break;
					}
				}

				if (req) {

					while (req) {

						bool changed = false;

						for (int i = 0; i < n; i++) {

							if (a[i] > x) {
								changed = true;
								swap(a[i], x);
								ans++;
								break;
							}
						}

						if (!changed) {
							poss = false;
							break;
						}

						req = false;

						for (int i = 0; i < n - 1; i++) {

							if (a[i + 1] < a[i]) {
								req = true;
								break;
							}
						}

						if (!req) {
							break;
						}
					}

				}
			}
		}

		if (poss) {

			cout << ans << endl;

		} else {

			cout << -1 << endl;

		}
	}
}