The Lost Gift#1576
Stan is shocked because he lost part of the precious gift Olie gave him. The gift consisted of two boxes filled with crystal balls. All the balls in one box were red, and all the balls in the other box were black. While giving the gift, Olie said with a sly smile: Stan! If you mix the balls from both boxes and randomly choose two, the probability that they are the same color is \frac{1}{2}.
Stan returned home happily with the two boxes, but he suddenly dropped the box with black balls, scattering them everywhere. Stan managed to collect at least of the black balls.
Given the number of red balls and the number of black balls Stan was able to collect, determine the number of black balls lost.
Each line contains two positive integers and , representing the number of red balls and the number of black balls found by Stan, respectively. The last line contains two zeroes and should not be processed.
For each test case, output the answer in a single line:
If the number of red balls is invalid according to the story, print No. of red balls invalid.
If the number of red balls is valid but the number of black balls is invalid, print No. of black balls invalid.
If both numbers and are valid, print all possible numbers of lost black balls as one or two integers in a single line, separated by a space and sorted in ascending order.
Example 1