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 $a_1, a_2, \ldots, a_n$. 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 $t$ ($1 \leq t \leq 10^4$): the number of test cases.

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

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ in the increasing order ($1 \leq a_1 < a_2 < \ldots < a_n < l$).

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 $\frac{|a-b|}{\max{(1, b)}} \leq 10^{-6}$.


-----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 $\frac{9-1}{2+1} = \frac{8}{3}$ seconds. So, the answer is equal to $1 + \frac{8}{3} = \frac{11}{3}$.

Difficulty: interview

Starter code:

Solutions:
import sys
import random
from fractions import Fraction
from math import *
 
def input():
    return sys.stdin.readline().strip()
 
def iinput():
    return int(input())

def finput():
    return float(input())

def tinput():
    return input().split()

def linput():
    return list(input())
 
def rinput():
    return list(map(int, tinput()))

def fiinput():
    return list(map(float, tinput()))
 
def rlinput():
    return list(map(int, input().split()))
def trinput():
    return tuple(rinput())

def srlinput():
    return sorted(list(map(int, input().split())))

def NOYES(fl):
    if fl:
        print("NO")
    else:
        print("YES")
def YESNO(fl):
    if fl:
        print("YES")
    else:
        print("NO")
    
def main():
    n, l = rinput()
    #n = iinput()
    #k = iinput() 
    #m = iinput() 
    #n = int(sys.stdin.readline().strip()) 
    #n, k = rinput()
    #n, m = rinput()
    #m, k = rinput()
    #n, k, m = rinput()
    #n, m, k = rinput()
    #k, n, m = rinput()
    #k, m, n = rinput() 
    #m, k, n = rinput()
    #m, n, k = rinput()
    q = rlinput()
    #q = linput()
    q = [0] + q + [l]
    w, e = [0] * (n + 2), [0] * (n + 2)
    
    for i in range(1, n + 2):
        e[n + 1 - i] = e[n + 2 - i] + ((q[-i] - q[-1 - i]) / i)
        w[i] = w[i - 1] + ((q[i] - q[i - 1]) / i)
        
    left, right = 0, n + 2
    while right > left + 1:
        mid = (right + left) // 2
        if w[mid] >= e[mid]:
            right = mid
        else:
            left = mid
            
    print((q[right] - q[right - 1] - (max(0, w[right - 1] - e[right]) * (n - right + 2) + max(0, e[right] - w[right - 1]) * right)) / (n + 2) + max(w[right - 1], e[right]))
        

            
        
    
                
    
    
    
            
    
        
    

for i in range(iinput()):
    main()


for __ in range(int(input())):
    n, l = list(map(int, input().split()))
    ar = list(map(int, input().split()))
    i, j = 0, n - 1
    x, y = 0, l
    v1, v2 = 1, 1
    ans = 0
    while i <= j and x < y:
        if (ar[i] - x) / v1 < (y - ar[j]) / v2:
            ans += (ar[i] - x) / v1
            y -= v2 * (ar[i] - x) / v1
            x = ar[i]
            v1 += 1
            i += 1
        else:
            ans += (y - ar[j]) / v2
            x += v1 * (y - ar[j]) / v2
            y = ar[j]
            v2 += 1
            j -= 1
    ans += (y - x) / (v1 + v2)
    print(ans)

for _ in range(int(input())):
  n,l=map(int,input().split())
  a=[0]+list(map(int,input().split()))+[l]
  b=[a[i+1]-a[i] for i in range(n+1)]
  ansl=0
  le=0
  lf=1
  ansr=0
  ri=n
  rf=1
  while le!=ri:
    if ansl+b[le]/lf<ansr+b[ri]/rf:
      ansl+=b[le]/lf
      le+=1
      lf+=1
    else:
      ansr+=b[ri]/rf
      ri-=1
      rf+=1
  t=b[le]
  ans=max(ansl,ansr)
  if ansl<ansr:
    t-=(ansr-ansl)*lf
  if ansl>ansr:
    t-=(ansl-ansr)*rf
  print(ans+t/(lf+rf))

import sys
input = sys.stdin.readline

def main():
    n, l = map(int, input().split())
    alst = list(map(int, input().split()))
    ll = 0
    rr = n - 1
    l_pos = 0
    r_pos = l
    l_speed = 1
    r_speed = 1
    ans = 0
    while rr >= ll:
        l2 = (alst[ll] - l_pos) * r_speed
        r2 = (r_pos - alst[rr]) * l_speed
        if r2 == l2:
            ans += (alst[ll] - l_pos) / l_speed
            r_pos = alst[rr]
            l_pos = alst[ll]
            r_speed += 1
            l_speed += 1
            rr -= 1
            ll += 1
        elif r2 < l2:
            ans += (r_pos - alst[rr]) / r_speed
            l_pos += (r_pos - alst[rr]) / r_speed * l_speed
            r_pos = alst[rr]
            r_speed += 1
            rr -= 1
        else:
            ans += (alst[ll] - l_pos) / l_speed
            r_pos -= (alst[ll] - l_pos) / l_speed * r_speed
            l_pos = alst[ll]
            l_speed += 1
            ll += 1

    ans += (r_pos - l_pos) / (r_speed + l_speed)
    print(ans)
    
for _ in range(int(input())):
    main()

from sys import stdin
input = stdin.readline


def myk(l, stops, czas):
    pos = 0
    v = 1.0
    for stop in stops:
        dist = stop - pos
        if czas * v > dist:
            czas -= dist/v
            pos = stop
            v += 1
        else:
            return pos + czas * v
    return pos + czas * v


def solve():
    n, l = [int(x) for x in input().split()]
    a = [int(x) for x in input().split()]
    b = [l - x for x in a[::-1]]
    pocz = 0.0
    kon = l/2.0
    eps = 1e-7
    while pocz + eps < kon:
        mid = (pocz + kon) / 2.0
        pos1 = myk(l, a, mid)
        pos2 = l - myk(l, b, mid)
        if pos1 < pos2:
            pocz = mid
        else:
            kon = mid
    print(kon)


t = int(input())

for _ in range(t):
    solve()

import sys

input = sys.stdin.readline

for _ in range(int(input())):
    n,l = list(map(int,input().split()))
    a = list(map(int,input().split()))
    a = [0] + a + [l]

    s = [0 for i in range(n+2)]
    e = [0 for i in range(n+2)]
    for i in range(1,n+2):
        s[i] = (a[i] - a[i-1])/i
        s[i] += s[i-1]
    a = a[::-1]
    for i in range(1,n+2):
        e[i] = (a[i-1] - a[i])/i
        e[i] += e[i-1]
    e = e[::-1]
    #print(s)
    #print(e)
    a = a[::-1]

    for i in range(1,n+2):
        if s[i]>=e[i]:
            #i-1~i
            #print(i)
            s_speed = i
            e_spped = n+2-i
            if s[i-1]<=e[i]:
                L = a[i] - a[i-1] - s_speed * (e[i] - s[i-1])
                t = L/(n+2)
                ans = e[i] + t
                print(ans)
                break
            else:
                L = a[i] - a[i-1] - e_spped * (s[i-1] - e[i])
                t = L/(n+2)
                ans = s[i-1] + t
                print(ans)
                break


t = int(input())
for i in range(t):
	n, l = list(map(int, input().split()))
	a = list(map(int, input().split()))
	tmp1 = 0
	tmp2 = n - 1
	t = 0
	v1 = 1
	v2 = 1
	x1 = 0
	x2 = l
	while (tmp2 - tmp1) > -1:
		t1 = (a[tmp1] - x1) / v1
		t2 = (x2 - a[tmp2]) / v2
		if t1 > t2:
			x1 += v1 * t2
			x2 -= v2 * t2
			v2 += 1
			t += t2
			tmp2 -= 1
		elif abs(t1 - t2) < 0.000000001:
			x1 += v1 * t1
			x2 -= v2 * t2
			v1 += 1
			v2 += 1
			t += t1
			tmp2 -= 1
			tmp1 += 1
		else:
			x1 += v1 * t1
			x2 -= v2 * t1
			v1 += 1
			t += t1
			tmp1 += 1
	t += (x2 - x1) / (v1 + v2)
	print("{:.07f}".format(t))
		


for _ in range(int(input())):
    n, l = list(map(int, input().split()))
    arr = list(map(int, input().split()))
    ls, rs, lx, rx, li, ri = 1, 1, 0, l, 0, n
    total = 0
    while li != ri:
        if (arr[li]-lx)/ls < (rx-arr[ri-1])/rs:
            total += (arr[li]-lx)/ls
            rx -= (arr[li]-lx)/ls*rs
            lx = arr[li]
            li += 1
            ls += 1
        else:
            total += (rx-arr[ri-1])/rs
            lx += (rx-arr[ri-1])/rs*ls
            rx = arr[ri-1]
            ri -= 1
            rs += 1
    total += (rx-lx)/(ls+rs)
    print(total)


import sys
input = sys.stdin.readline

from bisect import bisect_right

for _ in range(int(input())):
	n, l = list(map(int, input().split()))
	A = list(map(int, input().split()))

	c1 = []
	speed = 1
	x = 0
	t = 0.
	for a in A:
		t += (a-x)/speed
		c1.append(t)
		speed += 1
		x = a

	c2 = []
	speed = 1
	x = l
	t = 0.
	for a in reversed(A):
		t += (x-a)/speed
		c2.append(t)
		speed += 1
		x = a

	lo = 0.
	hi = float(l)

	while hi - lo > 1e-7:
		m = (lo + hi) / 2

		i1 = bisect_right(c1, m)-1
		if i1 == -1:
			x1 = m
		else:
			tpass = c1[i1]
			textra = m - tpass
			x1 = A[i1] + textra * (i1+2)

		i2 = bisect_right(c2, m)-1
		if i2 == -1:
			x2 = l-m
		else:
			tpass = c2[i2]
			textra = m - tpass
			x2 = A[-1-i2] - textra * (i2+2)

		if x1 < x2: lo = m
		else: hi = m

	print((lo+hi)/2)


y=lambda:[*map(int,input().split())]
for _ in range(int(input())):
    n,t=map(int,input().split())
    a=[0]+y()+[t]
    l,h=0,n+1
    tl=th=0
    while h-l>1:
        dl=(a[l+1]-a[l])/(l+1)
        dh=(a[h]-a[h-1])/(n+2-h)
        if tl+dl>th+dh:th+=dh;h-=1
        else:tl+=dl;l+=1
    sh,sl=n+2-h,l+1
    if tl>th:tl,th=th,tl;sh,sl=sl,sh
    print(th+(a[h]-a[l]-(th-tl)*sl)/(sh+sl))

import sys
input = lambda: sys.stdin.readline().rstrip()

T = int(input())
for _ in range(T):
    N, L = list(map(int, input().split()))
    N += 2
    A = [0] + [int(a) for a in input().split()] + [L]
    x1 = 0
    x2 = N - 1
    t1, t2 = 0, 0
    while x2 - x1 > 1:
        a1 = t1 + (A[x1+1] - A[x1]) / (x1 + 1)
        a2 = t2 + (A[x2] - A[x2-1]) / (N - x2)
        if a1 < a2:
            t1 = a1
            x1 += 1
        else:
            t2 = a2
            x2 -= 1
    if t1 < t2:
        ans = t2 + ((A[x2] - A[x1]) - (x1 + 1) * (t2 - t1)) / (x1 + 1 + N - x2)
    else:
        ans = t1 + ((A[x2] - A[x1]) - (N - x2) * (t1 - t2)) / (x1 + 1 + N - x2)
    print(ans)