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

2/2 Sample Input 00 01 02 03 04 Sample Output 0.000 0.500 0.727 0.861 0.954