When you rent a table at a pool hall, the proprietor gives you a 4-by-4 tray of 16 balls, as shown in Figure (a) below. One of these balls, called the \cue ball", is white, and the remaining 15 are numbered 1 through 15. At the beginning of a game, the numbered balls are racked up 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 x numbered balls. You'd like to be able to rack up the x numbered balls in a triangle, and have all x+1 balls perfectly ll a square m-by-m tray. For what values of x is this possible? In this problem you'll be given an lower bound a and upper bound b, and asked how many numbers within this range have the above property.

Input for each test case will one line containin two integers a b, where 0 < a < b <= 10^9. The line 0 0 will follow the last test case.

For each test case one line of output as follows: Case n: k if there are k integers x such that a < x + 1 < b, x balls can be racked up in a triangle, and x + 1 balls fill a square tray.

East Central North America 2011