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1154.   A Mathematical Curiosity
Time Limit: 1.0 Seconds   Memory Limit: 65536K
Total Runs: 6924   Accepted Runs: 2700    Multiple test files

Given two integers n and m, count the number of pairs of integers (a,b) such that 0 < a < b < n and (a2+b2+m)/(ab) is an integer.


You will be given a number of cases in the input. Each case is specified by a line containing the integers n and m. The end of input is indicated by a case in which n = m = 0. You may assume that 0 < n ≤ 100.


For each case, print the case number as well as the number of pairs (a,b) satisfying the given property. Print the output for each case on one line in the format as shown below.

Sample Input

10 1
20 3
30 4
0 0

Sample Output

Case 1: 2
Case 2: 4
Case 3: 5

Source: East Central North America 1999 Practice
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