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
import java.io.*;
import java.util.*;
import java.util.*;
import java.math.*;
public class Euler {

	static FastReader in;
	static PrintWriter o;
	static int[][] dp;

	public static void solve() {
		int n = in.nextInt();
		int x = in.nextInt();
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = in.nextInt();
		}
		dp = new int[501][501];
		for (int i = 0; i <= n; i++) Arrays.fill(dp[i], Integer.MAX_VALUE);
		int ans = dp(0, arr, x);
		if (ans == (int) 1e9) {
			o.println("-1");
		} else {
			o.println(ans);
		}

	}

	public static int dp(int i, int[] arr, int x) {
		if (i == arr.length) {
			return isSorted(arr, arr.length - 1) ? 0 : (int) 1e9;
		}
		if (!isSorted(arr, i)) {
			return (int) 1e9;
		}
		if (dp[i][x] != Integer.MAX_VALUE) {
			return dp[i][x];
		}
		int ans = (int) 1e9;
		if (arr[i] >= x) {
			int[] ar = arr.clone();
			ar[i] = x;
			ans = Math.min(dp(i+1, arr, x), 1 + dp(i+1, ar, arr[i]));
		} else {
			ans = dp(i + 1, arr, x);
		}
		dp[i][x] = ans;
		return ans;
	}

	public static boolean isSorted(int[] arr, int x) {
		for (int i = 1; i <= x; i++) {
			if (arr[i] < arr[i-1]) {
				return false;
			}
		}
		return true;
	}

	public static void main(String[] args) {
		in = new FastReader();
		o = new PrintWriter(System.out);

		int t = in.nextInt();
		while (t-- > 0) {
			solve();
		}


		o.close();
		return;
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		int[] readArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}

		long[] readLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++) a[i] = nextLong();
			return a;
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

}