B. Lattice of Resistors 

The Problem

Given an infinite 2D Lattice of resisters as shown below, where the resistance on each edge between neighboring junctions is exactly 1. Pick any junction O and assign the coordinate (0,0). What is the total resistance between O and some other junction J=(i,j)?

Hint: There is a surprising Dynamic Programming solution, but how do you get it to fit under the memory requirement? :-) .

The Input

A number of inputs. One testcase on each line. The input of each test case is simply the values i, j on a single line. All values will fit inside an unsigned 64 bit integer.

The Output

For each input value, output the total resistance between O and J on a single line. Round to 3 digits after the decimal.

Sample Input

0 0
0 1
0 2
0 3
0 4

Sample Output

0.000
0.500
0.727
0.861
0.954

Problem setter: Josh Bao
Alternative Solution: Mike Liu