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
// Nov 30, 2020
import java.util.*;
import java.io.*;

public class A {
	static class FastReader {

		BufferedReader br;
		StringTokenizer st;

		private 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());
		}

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

		int[] nextIntArrayOne(int n) {
			int[] a = new int[n + 1];
			for (int i = 1; i < n + 1; i++)
				a[i] = nextInt();
			return a;
		}

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

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
	static final int MAX = 100000;
	static int ans = MAX;
	
	public static void main(String[] args) {
		FastReader s = new FastReader();
		StringBuilder str = new StringBuilder();

		int t = s.nextInt();

		while (t-- > 0) {
			int n = s.nextInt(), x = s.nextInt();
			int arr[] = s.nextIntArray(n);
			int dp[][] =  new int[501][501];
			for(int d[] : dp) {
				Arrays.fill(d, -1);
			}
			solve(arr,0,x,0,dp);
			
			
			if(ans == MAX)
				str.append("-1\n");
			else
			str.append(ans +"\n");
			ans = MAX;
		}
		System.out.println(str);
	}
		
	private static int  solve(int[] arr, int i, int x, int count, int[][] dp) {
		
		if(i == arr.length) {
			
			for(int j = 1; j < arr.length ; j++) {
				if(arr[j] < arr[j - 1]) {
					return MAX;
				}
			}
			ans = Math.min(ans, count);
			return count;
		}
		
		if(dp[i][x] != -1) return dp[i][x];
		
		int a = Integer.MAX_VALUE, b= Integer.MAX_VALUE;
		if(arr[i] > x) {
			int temp = arr[i];
			arr[i] = x;
			a =  solve(arr, i + 1, temp, count + 1, dp);
			arr[i] = temp;
		}
		
		
		b = solve(arr,i + 1, x, count, dp);
		
		return dp[i][x] = Math.min(a, b);
	}

}
