Everyone out of the Pool#2678
When you rent a table at a pool hall, the proprietor gives you a -by- tray of balls, as shown in Figure (a) below. One of these balls, called the "cue ball", is white, and the remaining balls are numbered from to . At the beginning of a game, the numbered balls are racked in a triangle (without the cue ball), as shown in Figure (b).
Now imagine other pool-like games where you have a cue ball and numbered balls. You would like to be able to rack up the numbered balls in a triangle, and have all x + 1 balls perfectly fill a square -by- tray. For which values of is this possible? In this problem, you will be given a lower bound and upper bound , and asked how many numbers within this range have the above property.
Input for each test case will be one line containing two integers , where 0 < a < b \leq 10^9. The line will follow the last test case.
For each test case, output one line in the following format:
Case n: k
if there are integers such that a < x + 1 < b, balls can be arranged in a triangle, and x + 1 balls fill a square tray.
Example 1