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.util.*;

import java.io.*;
import java.math.*;
import java.awt.geom.*;

import static java.lang.Math.*;

public class Solution implements Runnable {

	long mod1 = (long) 1e9 + 7;
	int mod2 = 998244353;

	public void solve() throws Exception {
		int t = sc.nextInt();
		while (t-- > 0) {
			int k=sc.nextInt();
			int l=sc.nextInt();
			int arr[]=sc.readArray(k);
			double time1[]=new double[k];
			double time2[]=new double[k];
			double initialtime=0.0;
			double speed=1.0;
			double initialpos=0.0;
			for(int i=0;i<k;i++)
			{
				time1[i]=((double)(arr[i])-initialpos)/speed;
				if(i!=0) time1[i]=time1[i-1]+time1[i];
				speed+=1.0;
			    //out.print(time1[i]+" ");
				initialpos=(double)arr[i];
			}
			speed=1.0;
			initialpos=(double)l;
			for(int i=k-1;i>=0;i--)
			{
				time2[i]=((double)(initialpos-arr[i]))/speed;
				if(i!=k-1) time2[i]=time2[i+1]+time2[i];
				//out.print(time2[i]+" ");
				speed+=1.0;
				initialpos=(double)arr[i];
			}
			int index=-1;
			initialtime=0.0;
			boolean flag=true;
			
			if(time1[0]==time2[0])
			{
				out.println(time1[0]);
				continue;
			}
			if(time1[k-1]==time2[k-1])
			{
				out.println(time1[0]);
				continue;
			}
			if(time1[0]>time2[0])
			{
				double diss=time2[0];
				double extra=((double)arr[0]-diss)/(k+1+1);
				out.println(time2[0]+extra);
				continue;
			}
			if(time2[k-1]>time1[k-1])
			{
				double diss=l-time1[k-1];
				double extra=((double)diss-(double)arr[k-1])/(k+1+1);
				out.println(time1[k-1]+extra);
				continue;
			}
			
			for(int i=1;i<k;i++)
			{
				double right=time1[i];
				double left=time1[i-1];
				double right2=time2[i];
				double left2=time2[i-1];
				if(right2==right)
				{
					flag=false;
					out.println(right2);
					break;
				}
				if(left2==left)
				{
					flag=false;
					out.println(right2);
					break;
				}
				if(right2>right || left2<left)
					continue;
				double leftmark=(double)arr[i-1];
				double rightmark=(double)arr[i];
				int leftkaspeed=i+1;
				int rightkaspeed=k-i+1;
				double dd=0.0;
				if(left>=right2)
				{
					rightmark=rightmark-(left-right2)*rightkaspeed;
					double extratime=(rightmark-leftmark)/(double)(leftkaspeed+rightkaspeed);
					out.println(left+extratime);
					break;
				}
				else
				{
					leftmark=leftmark+(right2-left)*leftkaspeed;
					double extratime=(rightmark-leftmark)/(double)(leftkaspeed+rightkaspeed);
					out.println(right2+extratime);
					break;
				}
				
				
				
				
				
				
			}
			

		}

	}

	static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}

	static long ncr(int n, int r, long p) {
		if (r > n)
			return 0l;
		if (r > n - r)
			r = n - r;

		long C[] = new long[r + 1];

		C[0] = 1;

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

			for (int j = Math.min(i, r); j > 0; j--)
				C[j] = (C[j] + C[j - 1]) % p;
		}
		return C[r] % p;
	}

	public long power(long x, long y, long p) {
		long res = 1;
		// out.println(x+" "+y);
		x = x % p;
		if (x == 0)
			return 0;

		while (y > 0) {
			if ((y & 1) == 1)
				res = (res * x) % p;
			y = y >> 1;
			x = (x * x) % p;
		}
		return res;
	}

	static Throwable uncaught;

	BufferedReader in;
	FastScanner sc;
	PrintWriter out;

	@Override
	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			sc = new FastScanner(in);
			solve();
		} catch (Throwable uncaught) {
			Solution.uncaught = uncaught;
		} finally {
			out.close();
		}
	}

	public static void main(String[] args) throws Throwable {
		Thread thread = new Thread(null, new Solution(), "", (1 << 26));
		thread.start();
		thread.join();
		if (Solution.uncaught != null) {
			throw Solution.uncaught;
		}
	}

}

class FastScanner {

	BufferedReader in;
	StringTokenizer st;

	public FastScanner(BufferedReader in) {
		this.in = in;
	}

	public String nextToken() throws Exception {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(in.readLine());
		}
		return st.nextToken();
	}

	public int nextInt() throws Exception {
		return Integer.parseInt(nextToken());
	}

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

	public long nextLong() throws Exception {
		return Long.parseLong(nextToken());
	}

	public double nextDouble() throws Exception {
		return Double.parseDouble(nextToken());
	}

}