Migrated from Lutece 728 Everyone out of the Pool

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Description

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 fill 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

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

Output

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.

Samples

15 17
14 16
1 20
0 0

Case 1: 1
Case 2: 0
Case 3: 2

Resources

2011 East Central Regional Contest