Problem: There is a road with length l meters. The start of the road has coordinate 0, the end of the road has coordinate l.

There are two cars, the first standing at the start of the road and the second standing at the end of the road. They will start driving simultaneously. The first car will drive from the start to the end and the second car will drive from the end to the start.

Initially, they will drive with a speed of 1 meter per second. There are n flags at different coordinates a_1, a_2, …, a_n. Each time when any of two cars drives through a flag, the speed of that car increases by 1 meter per second.

Find how long will it take for cars to meet (to reach the same coordinate). 

Input

The first line contains one integer t (1 ≤ t ≤ 10^4): the number of test cases.

The first line of each test case contains two integers n, l (1 ≤ n ≤ 10^5, 1 ≤ l ≤ 10^9): the number of flags and the length of the road.

The second line contains n integers a_1, a_2, …, a_n in the increasing order (1 ≤ a_1 < a_2 < … < a_n < l).

It is guaranteed that the sum of n among all test cases does not exceed 10^5.

Output

For each test case print a single real number: the time required for cars to meet.

Your answer will be considered correct, if its absolute or relative error does not exceed 10^{-6}. More formally, if your answer is a and jury's answer is b, your answer will be considered correct if \frac{|a-b|}{max{(1, b)}} ≤ 10^{-6}.

Example

Input


5
2 10
1 9
1 10
1
5 7
1 2 3 4 6
2 1000000000
413470354 982876160
9 478
1 10 25 33 239 445 453 468 477


Output


3.000000000000000
3.666666666666667
2.047619047619048
329737645.750000000000000
53.700000000000000

Note

In the first test case cars will meet in the coordinate 5.

The first car will be in the coordinate 1 in 1 second and after that its speed will increase by 1 and will be equal to 2 meters per second. After 2 more seconds it will be in the coordinate 5. So, it will be in the coordinate 5 in 3 seconds.

The second car will be in the coordinate 9 in 1 second and after that its speed will increase by 1 and will be equal to 2 meters per second. After 2 more seconds it will be in the coordinate 5. So, it will be in the coordinate 5 in 3 seconds.

In the second test case after 1 second the first car will be in the coordinate 1 and will have the speed equal to 2 meters per second, the second car will be in the coordinate 9 and will have the speed equal to 1 meter per second. So, they will meet after (9-1)/(2+1) = 8/3 seconds. So, the answer is equal to 1 + 8/3 = 11/3.

Solution (in JAVA):

Solution:

import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.awt.*;

public class Main {

	static long sx = 0, sy = 0, mod = (long) (1e9 + 7);

	static ArrayList<Integer>[] a;
	static long[][] dp;
	static long[] fa;
	static long[] farr;
	public static PrintWriter out = new PrintWriter(System.out);
	static ArrayList<pair> pa = new ArrayList<>();
	static StringBuilder sb = new StringBuilder();
	static boolean cycle = false;
	static long m = 998244353;
	static long[] no, col;
	static String s;
	static long k = 0, n = 0, ans = 0;
	static long cnt;
	// static long[] dp;
	// static long[] p;
	// static long[] ans;
	// static Double[][] a = new Double[2][2];
	static Double[][] b = new Double[2][2];
	static Double[] x;
	static Double[] y;
	static long[] d;
	// static boolean b = true;
	static int[][] par;
	static int[] depth;
	static HashMap<Integer, Integer> map;
	static ArrayList<Integer> p;

	public static void main(String[] args) throws IOException {

		// Scanner scn = new Scanner(new BufferedReader(new
		// InputStreamReader(System.in)));

		Reader scn = new Reader();

		int t = scn.nextInt();

		while (t-- != 0) {

			int n = scn.nextInt();
			long l = scn.nextLong();

			double[] a = new double[n + 2];

			for (int i = 1; i <= n; i++)
				a[i] = scn.nextDouble();

			a[n + 1] = l;

			int i1 = 0, s1 = 1, i2 = n + 1, s2 = 1;
			double pos1 = 0, pos2 = l;

			double ans = 0;

			while (i1<i2) {

				if (i2 == i1 + 1) {

					ans += time(pos2-pos1, s1 + s2);
					break;
				}

				else {

					double t1 = time(a[i1 + 1] - pos1, s1);
					double t2 = time(pos2 - a[i2 - 1], s2);
					ans+=Math.min(t1, t2);

					if (t1 < t2) {
						s1++;
						i1++;
						pos1 = a[i1];

						pos2 -= t1 * s2;
					}
					
					else if(t1 == t2){
						s1++;
						i1++;
						pos1 = a[i1];
						
						s2++;
						i2--;
						pos2 = a[i2];
					}

					else {

						s2++;
						i2--;
						pos2 = a[i2];

						pos1 += t2 * s1;
					}
				}

			}

			System.out.printf("%.10f", ans);
			System.out.println();
		}

	}

	public static double time(double dis, double s) {
		return dis / s;
	}

	// _________________________TEMPLATE_____________________________________________________________

	// public static long lcm(long x, long y) {
	//
	// return (x * y) / gcd(x, y);
	// }
	//
	// private static long gcd(long x, long y) {
	// if (x == 0)
	// return y;
	//
	// return gcd(y % x, x);
	// }
	//
	// static class comp implements Comparator<Integer> {
	//
	// @Override
	// public int compare(Integer p1, Integer p2) {
	//
	// return p2 - p1;
	//
	// }
	// }
	//
	// }
	//
	// public static long pow(long a, long b) {
	//
	// if (b < 0)
	// return 0;
	// if (b == 0 || b == 1)
	// return (long) Math.pow(a, b);
	//
	// if (b % 2 == 0) {
	//
	// long ret = pow(a, b / 2);
	// ret = (ret % mod * ret % mod) % mod;
	// return ret;
	// }
	//
	// else {
	// return ((pow(a, b - 1) % mod) * a % mod) % mod;
	// }
	// }

	private static class pair implements Comparable<pair> {

		long a, b, c;

		// pair(long a, int b, long sum) {
		// val = a;
		// cnt = b;
		// this.sum = sum;
		// }
		//
		@Override
		public int compareTo(pair o) {

			return 1;

		}

		// @Override

		// public int hashCode() {
		// return val * 17 + cnt * 31;
		// }
		//
		// @Override
		//
		// public boolean equals(Object o) {
		//
		// pair p = (pair) o;
		// return this.val == p.val && this.cnt == p.cnt;
		// }

	}

	private static String reverse(String s) {

		return new StringBuilder(s).reverse().toString();
	}

	public static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException {
			byte[] buf = new byte[1000000 + 1]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}

		public int[] nextIntArray(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		public int[][] nextInt2DArray(int m, int n) throws IOException {
			int[][] arr = new int[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}

		public long[][] nextInt2DArrayL(int m, int n) throws IOException {
			long[][] arr = new long[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}
		// kickstart - Solution
		// atcoder - Main
	}

}