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 v_1. 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 v_2. 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, v_1, v_2 and k (1 ≤ n ≤ 10 000, 1 ≤ l ≤ 10^9, 1 ≤ v_1 < v_2 ≤ 10^9, 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.

Source: codeforces | Difficulty: HARD
Tags: Sorting

Mathematics


Solutions:
(n, l, v1, v2, k) = list(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)


RYIawuypxfFqJOW = map
RYIawuypxfFqJOL = int
RYIawuypxfFqJOg = input
RYIawuypxfFqJOi = print
(n, l, v1, v2, k) = RYIawuypxfFqJOW(RYIawuypxfFqJOL, RYIawuypxfFqJOg().split())
n = (n + k - 1) // k
a = (v2 - v1) / (v1 + v2)
t = l / v2 / (n - (n - 1) * a)
RYIawuypxfFqJOi(n * t + (n - 1) * a * t)


3
import sys
sys.setrecursionlimit(10 ** 9)

def bscheck(n, l, v1, v2, k, t):
	while True:
		if k > n:
			k = n
		if n == 0:
			return True
		if l / v2 > t:
			return False
		tx = (l - v1 * t) / (v2 - v1)
		ty = (tx * v2 - tx * v1) / (v1 + v2)
		_n = n - k
		_l = l - tx * v1 - ty * v1
		_t = t - tx - ty
		n = _n
		l = _l
		t = _t
(n, l, v1, v2, k) = list(map(int, input().split()))
(lt, rt) = (0, 1791791791)
for i in range(100):
	mid = (lt + rt) / 2
	if bscheck(n, l, v1, v2, k, mid):
		rt = mid
	else:
		lt = mid
print(rt)


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


(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)


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)))


import sys
(n, l, v1, v2, k) = list(map(int, input().split()))
n = (n + k - 1) // k
if n == 1:
	print(l / v2)
	return
(L, R) = (0, l)
for i in range(100):
	M = (L + R) / 2
	S = l - M
	T = M * (n * 2 - 1) - l
	if T * v1 > S * v2:
		R = M
	else:
		L = M
print(M / v2 + S / 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)


(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)


line = input().split()
a = []
for i in line:
	a.append(int(i))
if a[0] % a[4] == 0:
	m = a[0] // a[4] - 1
else:
	m = a[0] // a[4]
l = a[1]
v1 = a[2]
v2 = a[3]
d = l / (m * v1 * (1 / v2 + (1 - v1 / v2) / (v1 + v2)) + 1)
t = d / v2 + (l - d) / v1
print(t)


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)


(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(ans)


def main():
	(n, L, v1, v2, k) = map(int, input().split())
	group = (n + k - 1) // k
	(l, r) = (0, L)
	for _ in range(100):
		m = (l + r) / 2
		t2 = m / v2
		d = m - v1 * t2
		T = d / (v1 + v2)
		if v1 * (t2 + T) * (group - 1) + m <= L:
			l = m
		else:
			r = m
	ans = l / v2 + (L - l) / v1
	print('{0:.10f}'.format(ans))
main()


import math
(n, l, v1, v2, k) = map(int, input().split(' '))
p = math.ceil(n / k)

def calc(d):
	cyc = (d - d / v2 * v1) / (v1 + v2)
	t = cyc + d / v2
	ans = -1
	for i in range(p):
		tb4 = t * i
		db4 = tb4 * v1
		ans = max(ans, d / v2 + tb4 + max(0, l - d - db4) / v1)
	return ans
lo = 0
hi = 1000000000
for i in range(200):
	a1 = (2 * lo + hi) / 3
	a2 = (lo + 2 * hi) / 3
	if calc(a1) < calc(a2):
		hi = a2
	else:
		lo = a1
print(calc(lo))


(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))


import math
(n, L, v1, v2, k) = [int(x) for x in input().split()]
n = int(math.ceil(n / k))
a = v2 / v1
x = 2 * L / (a + 2 * n - 1)
y = L - (n - 1) * x
print((y * n + (n - 1) * (y - x)) / v2)


from sys import stdin, stdout
import math

def solution():
	(n, l, v1, v2, k) = map(int, stdin.readline().rstrip().split())
	grs = math.ceil(float(n) / k)
	c = grs / (v2 - v1) + (grs - 1) / (v1 + v2)
	stdout.write('{}'.format(l / (v1 + 1 / c)))

def __starting_point():
	solution()
__starting_point()


raw = input().split()
import decimal
n = int(raw[0])
k = int(raw[4])

def get(n, k):
	if n % k == 0:
		return n // k
	else:
		return n // k + 1
n = decimal.Decimal(str(get(n, k)))
l = decimal.Decimal(str(raw[1]))
v1 = decimal.Decimal(str(raw[2]))
v2 = decimal.Decimal(str(raw[3]))
print(l / v2 * (decimal.Decimal('1') + decimal.Decimal('2') * (n - decimal.Decimal(1)) * (v2 - v1) / (decimal.Decimal(2) * v1 * n + v2 - v1)))


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))


(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)


(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)


import math
import random
import heapq, bisect
import sys
from collections import deque, defaultdict
from fractions import Fraction
import sys
import threading
from collections import defaultdict
threading.stack_size(10 ** 8)
mod = 10 ** 9 + 7
mod1 = 998244353
import os
import sys
from io import BytesIO, IOBase
sys.setrecursionlimit(300000)
BUFSIZE = 8192

class FastIO(IOBase):
	newlines = 0

	def __init__(self, file):
		self._fd = file.fileno()
		self.buffer = BytesIO()
		self.writable = 'x' in file.mode or 'r' not in file.mode
		self.write = self.buffer.write if self.writable else None

	def read(self):
		while True:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			if not b:
				break
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines = 0
		return self.buffer.read()

	def readline(self):
		while self.newlines == 0:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			self.newlines = b.count(b'\n') + (not b)
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines -= 1
		return self.buffer.readline()

	def flush(self):
		if self.writable:
			os.write(self._fd, self.buffer.getvalue())
			(self.buffer.truncate(0), self.buffer.seek(0))

class IOWrapper(IOBase):

	def __init__(self, file):
		self.buffer = FastIO(file)
		self.flush = self.buffer.flush
		self.writable = self.buffer.writable
		self.write = lambda s: self.buffer.write(s.encode('ascii'))
		self.read = lambda : self.buffer.read().decode('ascii')
		self.readline = lambda : self.buffer.readline().decode('ascii')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')

class TreeNode:

	def __init__(self, k, v):
		self.key = k
		self.value = v
		self.left = None
		self.right = None
		self.parent = None
		self.height = 1
		self.num_left = 1
		self.num_total = 1

class AvlTree:

	def __init__(self):
		self._tree = None

	def add(self, k, v):
		if not self._tree:
			self._tree = TreeNode(k, v)
			return
		node = self._add(k, v)
		if node:
			self._rebalance(node)

	def _add(self, k, v):
		node = self._tree
		while node:
			if k < node.key:
				if node.left:
					node = node.left
				else:
					node.left = TreeNode(k, v)
					node.left.parent = node
					return node.left
			elif node.key < k:
				if node.right:
					node = node.right
				else:
					node.right = TreeNode(k, v)
					node.right.parent = node
					return node.right
			else:
				node.value = v
				return

	@staticmethod
	def get_height(x):
		return x.height if x else 0

	@staticmethod
	def get_num_total(x):
		return x.num_total if x else 0

	def _rebalance(self, node):
		n = node
		while n:
			lh = self.get_height(n.left)
			rh = self.get_height(n.right)
			n.height = max(lh, rh) + 1
			balance_factor = lh - rh
			n.num_total = 1 + self.get_num_total(n.left) + self.get_num_total(n.right)
			n.num_left = 1 + self.get_num_total(n.left)
			if balance_factor > 1:
				if self.get_height(n.left.left) < self.get_height(n.left.right):
					self._rotate_left(n.left)
				self._rotate_right(n)
			elif balance_factor < -1:
				if self.get_height(n.right.right) < self.get_height(n.right.left):
					self._rotate_right(n.right)
				self._rotate_left(n)
			else:
				n = n.parent

	def _remove_one(self, node):
		replacement = node.left or node.right
		if node.parent:
			if AvlTree._is_left(node):
				node.parent.left = replacement
			else:
				node.parent.right = replacement
			replacement.parent = node.parent
			node.parent = None
		else:
			self._tree = replacement
			replacement.parent = None
		node.left = None
		node.right = None
		node.parent = None
		self._rebalance(replacement)

	def _remove_leaf(self, node):
		if node.parent:
			if AvlTree._is_left(node):
				node.parent.left = None
			else:
				node.parent.right = None
			self._rebalance(node.parent)
		else:
			self._tree = None
		node.parent = None
		node.left = None
		node.right = None

	def remove(self, k):
		node = self._get_node(k)
		if not node:
			return
		if AvlTree._is_leaf(node):
			self._remove_leaf(node)
			return
		if node.left and node.right:
			nxt = AvlTree._get_next(node)
			node.key = nxt.key
			node.value = nxt.value
			if self._is_leaf(nxt):
				self._remove_leaf(nxt)
			else:
				self._remove_one(nxt)
			self._rebalance(node)
		else:
			self._remove_one(node)

	def get(self, k):
		node = self._get_node(k)
		return node.value if node else -1

	def _get_node(self, k):
		if not self._tree:
			return None
		node = self._tree
		while node:
			if k < node.key:
				node = node.left
			elif node.key < k:
				node = node.right
			else:
				return node
		return None

	def get_at(self, pos):
		x = pos + 1
		node = self._tree
		while node:
			if x < node.num_left:
				node = node.left
			elif node.num_left < x:
				x -= node.num_left
				node = node.right
			else:
				return (node.key, node.value)
		raise IndexError('Out of ranges')

	@staticmethod
	def _is_left(node):
		return node.parent.left and node.parent.left == node

	@staticmethod
	def _is_leaf(node):
		return node.left is None and node.right is None

	def _rotate_right(self, node):
		if not node.parent:
			self._tree = node.left
			node.left.parent = None
		elif AvlTree._is_left(node):
			node.parent.left = node.left
			node.left.parent = node.parent
		else:
			node.parent.right = node.left
			node.left.parent = node.parent
		bk = node.left.right
		node.left.right = node
		node.parent = node.left
		node.left = bk
		if bk:
			bk.parent = node
		node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
		node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
		node.num_left = 1 + self.get_num_total(node.left)

	def _rotate_left(self, node):
		if not node.parent:
			self._tree = node.right
			node.right.parent = None
		elif AvlTree._is_left(node):
			node.parent.left = node.right
			node.right.parent = node.parent
		else:
			node.parent.right = node.right
			node.right.parent = node.parent
		bk = node.right.left
		node.right.left = node
		node.parent = node.right
		node.right = bk
		if bk:
			bk.parent = node
		node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
		node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
		node.num_left = 1 + self.get_num_total(node.left)

	@staticmethod
	def _get_next(node):
		if not node.right:
			return node.parent
		n = node.right
		while n.left:
			n = n.left
		return n

class SegmentTree1:

	def __init__(self, data, default=2 ** 51, func=lambda a, b: a & b):
		self._default = default
		self._func = func
		self._len = len(data)
		self._size = _size = 1 << (self._len - 1).bit_length()
		self.data = [default] * (2 * _size)
		self.data[_size:_size + self._len] = data
		for i in reversed(range(_size)):
			self.data[i] = func(self.data[i + i], self.data[i + i + 1])

	def __delitem__(self, idx):
		self[idx] = self._default

	def __getitem__(self, idx):
		return self.data[idx + self._size]

	def __setitem__(self, idx, value):
		idx += self._size
		self.data[idx] = value
		idx >>= 1
		while idx:
			self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
			idx >>= 1

	def __len__(self):
		return self._len

	def query(self, start, stop):
		if start == stop:
			return self.__getitem__(start)
		stop += 1
		start += self._size
		stop += self._size
		res = self._default
		while start < stop:
			if start & 1:
				res = self._func(res, self.data[start])
				start += 1
			if stop & 1:
				stop -= 1
				res = self._func(res, self.data[stop])
			start >>= 1
			stop >>= 1
		return res

	def __repr__(self):
		return 'SegmentTree({0})'.format(self.data)

class SegmentTree:

	def __init__(self, data, default=0, func=lambda a, b: a + b):
		self._default = default
		self._func = func
		self._len = len(data)
		self._size = _size = 1 << (self._len - 1).bit_length()
		self.data = [default] * (2 * _size)
		self.data[_size:_size + self._len] = data
		for i in reversed(range(_size)):
			self.data[i] = func(self.data[i + i], self.data[i + i + 1])

	def __delitem__(self, idx):
		self[idx] = self._default

	def __getitem__(self, idx):
		return self.data[idx + self._size]

	def __setitem__(self, idx, value):
		idx += self._size
		self.data[idx] = value
		idx >>= 1
		while idx:
			self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
			idx >>= 1

	def __len__(self):
		return self._len

	def query(self, start, stop):
		if start == stop:
			return self.__getitem__(start)
		stop += 1
		start += self._size
		stop += self._size
		res = self._default
		while start < stop:
			if start & 1:
				res = self._func(res, self.data[start])
				start += 1
			if stop & 1:
				stop -= 1
				res = self._func(res, self.data[stop])
			start >>= 1
			stop >>= 1
		return res

	def __repr__(self):
		return 'SegmentTree({0})'.format(self.data)

class Factorial:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorials = [1, 1]
		self.invModulos = [0, 1]
		self.invFactorial_ = [1, 1]

	def calc(self, n):
		if n <= -1:
			print('Invalid argument to calculate n!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.factorials):
			return self.factorials[n]
		nextArr = [0] * (n + 1 - len(self.factorials))
		initialI = len(self.factorials)
		prev = self.factorials[-1]
		m = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * i % m
		self.factorials += nextArr
		return self.factorials[n]

	def inv(self, n):
		if n <= -1:
			print('Invalid argument to calculate n^(-1)')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		p = self.MOD
		pi = n % p
		if pi < len(self.invModulos):
			return self.invModulos[pi]
		nextArr = [0] * (n + 1 - len(self.invModulos))
		initialI = len(self.invModulos)
		for i in range(initialI, min(p, n + 1)):
			next = -self.invModulos[p % i] * (p // i) % p
			self.invModulos.append(next)
		return self.invModulos[pi]

	def invFactorial(self, n):
		if n <= -1:
			print('Invalid argument to calculate (n^(-1))!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.invFactorial_):
			return self.invFactorial_[n]
		self.inv(n)
		nextArr = [0] * (n + 1 - len(self.invFactorial_))
		initialI = len(self.invFactorial_)
		prev = self.invFactorial_[-1]
		p = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * self.invModulos[i % p] % p
		self.invFactorial_ += nextArr
		return self.invFactorial_[n]

class Combination:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorial = Factorial(MOD)

	def ncr(self, n, k):
		if k < 0 or n < k:
			return 0
		k = min(k, n - k)
		f = self.factorial
		return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD

def powm(a, n, m):
	if a == 1 or n == 0:
		return 1
	if n % 2 == 0:
		s = powm(a, n // 2, m)
		return s * s % m
	else:
		return a * powm(a, n - 1, m) % m

def sort_list(list1, list2):
	zipped_pairs = zip(list2, list1)
	z = [x for (_, x) in sorted(zipped_pairs)]
	return z

def product(l):
	por = 1
	for i in range(len(l)):
		por *= l[i]
	return por

def binarySearchCount(arr, n, key):
	left = 0
	right = n - 1
	count = 0
	while left <= right:
		mid = int((right + left) / 2)
		if arr[mid] < key:
			count = mid + 1
			left = mid + 1
		else:
			right = mid - 1
	return count

def countdig(n):
	c = 0
	while n > 0:
		n //= 10
		c += 1
	return c

def binary(x, length):
	y = bin(x)[2:]
	return y if len(y) >= length else '0' * (length - len(y)) + y

def countGreater(arr, n, k):
	l = 0
	r = n - 1
	leftGreater = n
	while l <= r:
		m = int(l + (r - l) / 2)
		if arr[m] >= k:
			leftGreater = m
			r = m - 1
		else:
			l = m + 1
	return n - leftGreater
(n, l, v1, v2, k) = map(int, input().split())
n = int(math.ceil(n / k))
r = v2 / v1
x = l * (r + 1)
x /= 2 * n + r - 1
ans = (n - 1) * 2 * x / (r + 1)
ans += x / r
print(ans / 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))


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())


(n, l, v, o, k) = list(map(int, input().split()))
T = (n + k - 1) // k
e = 1 - v / o
L = l / v / (T / o + T * e / (v + o) - e / (v + o) - 1 / o + 1 / v)
print((l - L) / v + L / o)


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))


import sys
import math
data = sys.stdin.read()
data = data.split(' ')
n = int(data[0])
l = int(data[1])
w = int(data[2])
v = int(data[3])
k = int(data[4])
z = math.ceil(n / k)
top = l / w - l / (2 * w * z) + l / (2 * v * z)
bot = 1 + v / (2 * w * z) - 1 / (2 * z)
print(top / bot)


(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)


(n, l, v1, v2, k) = map(int, input().split())
if k >= n:
	res = l / v2
else:
	(L, R) = (0, l / v2)
	x = (n + k - 1) // k
	for i in range(100):
		M = (L + R) / 2
		first = M + (l - v2 * M) / v1
		prev_cost = (x - 1) * (M + M * (v2 - v1) / (v1 + v2))
		last = prev_cost + (l - v1 * prev_cost) / v2
		if last > first:
			R = M
		else:
			L = M
	res = (l - L * v2) / v1 + L
print('{:0.10f}'.format(res))


(n, s, v1, v2, k) = map(int, input().split())
n = (n + k - 1) // k
(l, r, m) = (0, 1000000000000000000, 0)
for _ in range(300):
	m = (l + r) / 2
	y = (s - v1 * m) / (v2 - v1)
	gap = y * (v2 - v1)
	pikap = gap / (v1 + v2)
	if pikap * (n - 1) + n * y <= m:
		r = m
	else:
		l = m
print('%.10f' % r)


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))