CODE FESTIVAL 2016 Relay (Parallel) - Equivalent Resistance

In an electric circuit, when two resistors R_1 and R_2 are connected in parallel, the equivalent resistance R_3 can be derived from the following formula:

* \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{R_3}



Given R_1 and R_2, find R_3.

Constraints

* 1 \leq R_1, R_2 \leq 100
* R_1 and R_2 are integers.

Input

The input is given from Standard Input in the following format:


R_1 R_2


Output

Print the value of R_3.

The output is considered correct if the absolute or relative error is at most 10^{-6}.

Examples

Input

2 3


Output

1.2000000000


Input

100 99


Output

49.7487437186

Source: atcoder | Difficulty: UNKNOWN_DIFFICULTY


Solutions:
(r1, r2) = map(int, input().split())
print(r1 * r2 / (r1 + r2))


from collections import defaultdict

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

def main():
	(R1, R2) = getlist()
	ans = R1 * R2 / (R1 + R2)
	print(ans)
main()


(a, b) = map(int, input().split())
print(1 / (1 / a + 1 / b))


(a, b) = map(int, input().split())
print('{:0.10f}'.format(a * b / (a + b)))


a = list(map(int, input().split()))
print(1 / (1 / a[0] + 1 / a[1]))


(R1, R2) = map(int, input().split())
print(R1 * R2 / (R1 + R2))


def main():
	(n, m) = map(int, input().split())
	print(1 / (1 / n + 1 / m))
main()


(a, b) = (int(i) for i in input().split())
print(a * b * 1.0 / (a + b))


import sys

def input():
	return sys.stdin.readline().strip()

def list2d(a, b, c):
	return [[c] * b for i in range(a)]

def list3d(a, b, c, d):
	return [[[d] * c for j in range(b)] for i in range(a)]

def list4d(a, b, c, d, e):
	return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]

def ceil(x, y=1):
	return int(-(-x // y))

def INT():
	return int(input())

def MAP():
	return map(int, input().split())

def LIST(N=None):
	return list(MAP()) if N is None else [INT() for i in range(N)]

def Yes():
	print('Yes')

def No():
	print('No')

def YES():
	print('YES')

def NO():
	print('NO')
sys.setrecursionlimit(10 ** 9)
INF = 10 ** 18
MOD = 10 ** 9 + 7
(R1, R2) = MAP()
ans = 1 / (1 / R1 + 1 / R2)
print(ans)


(r1, r2) = map(int, input().split())
a = r1 * r2
b = r1 + r2
r3 = a / b
print(r3)


from fractions import *
(r1, r2) = map(int, input().split())
R1 = Fraction(1, r1)
R2 = Fraction(1, r2)
R3 = R1 + R2
print(R3.denominator / R3.numerator)


import math, string, itertools, fractions, heapq, collections, re, array, bisect, sys, random, time, copy, functools
sys.setrecursionlimit(10 ** 7)
inf = 10 ** 20
eps = 1.0 / 10 ** 15
mod = 10 ** 9 + 7

def LI():
	return [int(x) for x in sys.stdin.readline().split()]

def LI_():
	return [int(x) - 1 for x in sys.stdin.readline().split()]

def LF():
	return [float(x) for x in sys.stdin.readline().split()]

def LS():
	return sys.stdin.readline().split()

def I():
	return int(sys.stdin.readline())

def F():
	return float(sys.stdin.readline())

def S():
	return input()

def pf(s):
	return print(s, flush=True)

def main():
	(a, b) = LI()
	return 1 / (1 / a + 1 / b)
print(main())


def main():
	(r1, r2) = map(int, input().split())
	return r1 * r2 / (r1 + r2)
print(main())


(R1, R2) = map(int, input().split())
R = 1 / (1 / R1 + 1 / R2)
print(R)


def main():
	(R1, R2) = map(int, input().split())
	ans = R1 * R2 / (R1 + R2)
	print(ans)
main()


(r1, r2) = [int(v) for v in input().split()]
print(r1 * r2 / (r1 + r2))


(r_1, r_2) = map(int, input().split())
r_3 = r_1 * r_2 / (r_1 + r_2)
print(r_3)


(a, b) = map(int, input().split())
S = a + b
print(float(a * b / S))


import sys
(r1, r2) = list(map(int, sys.stdin.readline().strip().split(' ')))
R = 1 / r1 + 1 / r2
print(1 / R)


(r1, r2) = [int(item) for item in input().split()]
print(r1 * r2 / (r1 + r2))


(R1, R2) = [int(i) for i in input().split()]
R3 = 1 / (1 / R1 + 1 / R2)
print('{:.9f}'.format(R3))


(n, m) = map(float, input().split())
print(n * m / (n + m))


(r, t) = map(int, input().split())
print(1 / (1 / r + 1 / t))


(A, B) = map(int, input().split())
print(A * B / (A + B))


import math
import sys

def getinputdata():
	array_result = []
	data = input()
	array_result.append(data.split(' '))
	flg = 1
	try:
		while flg:
			data = input()
			array_temp = []
			if data != '':
				array_result.append(data.split(' '))
				flg = 1
			else:
				flg = 0
	finally:
		return array_result
arr_data = getinputdata()
r1 = int(arr_data[0][0])
r2 = int(arr_data[0][1])
print(1 / ((r2 + r1) / (r1 * r2)))


(x, y) = map(int, input().split())
print(x * y / (x + y))


(n, m) = map(int, input().split())
print(n * m / (n + m))


(r1, r2) = map(float, input().split())
r3 = r1 * r2 / (r1 + r2)
print(r3)


print(eval('1/' + input().replace(' ', '+1/')) ** (-1))


(r1, r2) = map(int, input().split())
print('%.6f' % (1 / (1 / r1 + 1 / r2)))


(r1, r2) = map(int, input().split())
r3 = r1 * r2 / (r1 + r2)
print(str(r3))