On vacations n pupils decided to go on excursion and gather all together. They need to overcome the path with the length l meters. Each of the pupils will go with the speed equal to v1. To get to the excursion quickly, it was decided to rent a bus, which has seats for k people (it means that it can't fit more than k people at the same time) and the speed equal to v2. In order to avoid seasick, each of the pupils want to get into the bus no more than once.

Determine the minimum time required for all n pupils to reach the place of excursion. Consider that the embarkation and disembarkation of passengers, as well as the reversal of the bus, take place immediately and this time can be neglected. 

Input

The first line of the input contains five positive integers n, l, v1, v2 and k (1 ≤ n ≤ 10 000, 1 ≤ l ≤ 109, 1 ≤ v1 < v2 ≤ 109, 1 ≤ k ≤ n) — the number of pupils, the distance from meeting to the place of excursion, the speed of each pupil, the speed of bus and the number of seats in the bus. 

Output

Print the real number — the minimum time in which all pupils can reach the place of excursion. Your answer will be considered correct if its absolute or relative error won't exceed 10 - 6.

Examples

Input

5 10 1 2 5


Output

5.0000000000


Input

3 6 1 2 1


Output

4.7142857143

Note

In the first sample we should immediately put all five pupils to the bus. The speed of the bus equals 2 and the distance is equal to 10, so the pupils will reach the place of excursion in time 10 / 2 = 5.

Difficulty: HARD
Tags: Sorting

Mathematics
Skill types: Sorting

Starter code:

Solutions:
(n, l, v1, v2, k) = map(int, input().split())
n = (n + k - 1) // k
t0 = l / v1
t1 = l / v2
if n == 1:
	print(t1)
else:
	for k in range(50):
		t = (t0 + t1) / 2
		d2 = v2 * t
		x2 = (d2 - l) / (n - 1) / 2
		u2 = (d2 - (n - 1) * x2) / n
		tt = u2 / v2 + (l - u2) / v1
		if tt > t:
			t1 = t
		else:
			t0 = t
	print(t)


import sys
eps = 1e-06

def solve(n, l, v1, v2):
	t2 = 1.0 * (v1 + v2) * l / (n * (v1 + v2) * v2 - (n - 1) * v2 * (v2 - v1))
	l2 = v2 * t2
	l1 = l - l2
	t1 = l1 / v1
	return t1 + t2
(n, t, v1, v2, k) = map(int, input().split())
n = (n + k - 1) // k
print(solve(n, t, v1, v2))


def binSearch(n, L, v1, v2, k):
	l = 0
	r = L
	while r - l > 1e-06:
		d = (l + r) / 2
		td = d / v1
		S = v2 * td
		g = d - S
		tb = g / (v1 + v2)
		b = v1 * tb
		if n % k == 0:
			a = n // k
		else:
			a = n // k + 1
		if a * d - b * (a - 1) > L:
			r = d
		else:
			l = d
	td = l / v1
	S = v2 * td
	g = l - S
	tb = g / (v1 + v2)
	b = v1 * tb
	return l / v1 + (L - l) / v2
(n1, L1, v11, v21, k1) = map(int, input().split())
print('{0:.10f}'.format(binSearch(n1, L1, v21, v11, k1)))


(n, l, v1, v2, k) = map(int, input().split())
grps = n // k + int(n % k > 0)
r = 1 - (v2 - v1) * 1.0 / (v1 + v2)
bd = l / (1 + (grps - 1) * r)
print(bd / v2 + (l - bd) / v1)


array = list(map(int, input().split()))
n = int(array[0])
l = int(array[1])
v1 = int(array[2])
v2 = int(array[3])
k = int(array[4])
bus = n // k
if n % k != 0:
	bus += 1
V = v1 + v2 + 2 * v2 * (bus - 1)
U = v1 + v2 + 2 * v1 * (bus - 1)
print(l * V / U / v2)


import math
inputParams = input().split()
n = int(inputParams[0])
l = int(inputParams[1])
v1 = int(inputParams[2])
v2 = int(inputParams[3])
k = int(inputParams[4])
times = math.ceil(n / k)
t1 = l / (v2 + 2 * v2 / (v2 + v1) * v1 * (times - 1))
totalTime = t1 + 2 * v2 / (v1 + v2) * t1 * (times - 1)
print(str(totalTime))


(n, l, v1, v2, k) = [int(x) for x in input().split()]
x = (n + k - 1) // k
print((l - l / v1 / (x / (v2 - v1) + (x - 1) / (v2 + v1) + 1 / v1)) / v1)


s = input()
li = s.split()
n = int(li[0])
l = int(li[1])
v1 = int(li[2])
v2 = int(li[3])
k = int(li[4])
t = n // k
if n % k != 0:
	t += 1
a = (v1 + v2) * l / (v1 + v2 + 2 * (t - 1) * v1)
ans = a / v2 + (l - a) / v1
print('{0:.10f}'.format(ans))


(n, l, a, b, k) = map(int, input().split())
m = n // k
if n % k != 0:
	m += 1
A = b + a + 2 * b * (m - 1)
B = b + a + 2 * a * (m - 1)
print(l * A / (b * B))


(n, l, v1, v2, k) = map(int, input().split())
m = (n - 1) // k + 1
v = v1 + v2
x = l * v * v2 / (m * v * v2 - (m - 1) * (v2 - v1) * v2)
print(x / v2 + (l - x) / v1)


(n, L, v1, v2, k) = map(int, input().split())
n = (n + k - 1) // k * 2
dif = v2 - v1
p1 = (n * v2 - dif) * L
p2 = (n * v1 + dif) * v2
ans = p1 / p2
print('%.7f' % ans)


(n, l, v1, v2, k) = map(int, input().split())
diff = v2 - v1
n = (n + k - 1) // k * 2
p1 = (n * v2 - diff) * l
p2 = (n * v1 + diff) * v2
print(p1 / p2)


(n, l, v1, v2, k) = map(int, input().split())
col = (n + k - 1) // k
m = l / (1 + 2 * (col - 1) * v1 / (v1 + v2))
print(m / v2 + (l - m) / v1)


(n, l, v1, v2, k) = list(map(int, input().split()))
n = (n + k - 1) // k
t = l / ((v1 + (v2 - v1) * v1 / (v1 + v2)) * (n - 1) + v2)
print(t * n + t * (v2 - v1) / (v1 + v2) * (n - 1))


import math
(n, l, v1, v2, k) = map(int, input().split(' '))
if n <= k:
	print(l / v2)
else:
	f = math.ceil(n / k)
	x = (v2 - v1) / (2 * v1)
	a = l / (f + x)
	b = x * a
	t = (f * (a + b) + (f - 1) * b) / v2
	print(t)


tmp = input()
tmp = tmp.split(' ')
n = int(tmp[0])
l = int(tmp[1])
v1 = int(tmp[2])
v2 = int(tmp[3])
k = int(tmp[4])

def canGo(timeLimit):
	t1 = (l - v2 * timeLimit) / (v1 - v2)
	t2 = timeLimit - t1
	timeSpent = 0
	pupilLeft = n
	busPos = 0
	pupilPos = 0
	while timeSpent + 5e-07 < timeLimit:
		if pupilLeft <= 0:
			return True
		timeToMeet = (busPos - pupilPos) / (v1 + v2)
		timeSpent = timeSpent + timeToMeet
		if timeSpent + 5e-07 > timeLimit:
			return False
		busPos = busPos - v2 * timeToMeet
		pupilPos = pupilPos + v1 * timeToMeet
		pupilLeft = pupilLeft - k
		timeSpent = timeSpent + t2
		if timeSpent + 5e-07 > timeLimit:
			return False
		pupilPos = pupilPos + v1 * t2
		busPos = busPos + v2 * t2
	if pupilLeft <= 0:
		return False
	else:
		return True

def bsearch():
	right = l / v1
	left = l / v2
	while left + 5e-07 < right:
		mid = (left + right) / 2
		result = canGo(mid)
		if result:
			right = mid
		else:
			left = mid
	return left
print(bsearch())


import math
(n, l, v1, v2, k) = map(int, input().split())
times = math.ceil(n / k)
t1 = l / (v2 + 2 * v2 / (v2 + v1) * v1 * (times - 1))
totalTime = t1 + 2 * v2 / (v1 + v2) * t1 * (times - 1)
print(str(totalTime))