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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

/**
 * @author b
 *
 */
public class D {

	private static Scanner scanner;
	private static PrintWriter writer;

	public static void main(String[] args) {
		scanner = new Scanner();
		writer = new PrintWriter(System.out);
		int tests = scanner.nextInt();
		for (int i = 0; i < tests; i++) {
			solve();
		}
		writer.close();
	}

	private static void solve() {

		int n = scanner.nextInt();
		int x = scanner.nextInt();
		int[] vals = scanner.nextIntArr(n);
		boolean[] outOfOrder = new boolean[n];
		Arrays.fill(outOfOrder, false);

		boolean isOk = true;
		for (int i=1; i < n; i++) {
			if (vals[i-1] > vals[i]) {
				isOk = false;
				break;
			}
		}

		if (isOk || n == 1) {
			writer.println(0);
			return;
		}


		for (int i=1; i < n; i++) {
			outOfOrder[i-1] = vals[i-1] > vals[i];
			if (i >= 2 && outOfOrder[i-1] && outOfOrder[i-2]) {
				writer.println(-1);
				return;
			}
		}
		int lastOutOfOrder = n-1;
		while (lastOutOfOrder >= 0 && !outOfOrder[lastOutOfOrder--]) {
		}
		lastOutOfOrder++;
		int steps = 0;
		for (int i=0; i < n; i++) {
			if (vals[i] > x && i <= lastOutOfOrder) {
				steps++;
				int tmp = vals[i];
				vals[i] = x;
				x = tmp;
			}
			if (i > 0 && vals[i-1] > vals[i]) {
				writer.println(-1);
				return;
			}
		}

		writer.println(steps);
	}

	@SuppressWarnings("unused")
	private static void print(String... args) {

		for (String arg : args) {

			writer.print(arg + " ");
		}
		writer.println();
	}

	// Props to SecondThread
	static class Scanner {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer tokenizer = new StringTokenizer("");

		String next() {
			while (!tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return tokenizer.nextToken();
		}

		long[] nextLongArr(int num) {
			long[] vals = new long[num];
			for (int i = 0; i < num; i++)
				vals[i] = nextLong();
			return vals;
		}

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

		int[] nextIntArr(int numberOfElements) {
			int[] values = new int[numberOfElements];
			for (int i = 0; i < numberOfElements; i++)
				values[i] = nextInt();
			return values;
		}

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

}
