编程题：A Mathematical Curiosity
Given two integers n and m, count the number of pairs of integers $(a,b)$ such that $0 < a < b < n$ and $(a^2+b^2 +m)/(ab)$ is an integer.
This problem contains multiple test cases!
### 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 $0 < n <= 100$，$0 < m <= 100$.
### Output:
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:
in
10 1
20 3
30 4
0 0
in
4 2
2 1
0 0
### Sample Output:
out
Case 1: 2
Case 2: 4
Case 3: 5
out
Case 1: 1
Case 2: 0
answer：若无答案欢迎评论
This problem contains multiple test cases!
### 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 $0 < n <= 100$，$0 < m <= 100$.
### Output:
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:
in
10 1
20 3
30 4
0 0
in
4 2
2 1
0 0
### Sample Output:
out
Case 1: 2
Case 2: 4
Case 3: 5
out
Case 1: 1
Case 2: 0
answer：若无答案欢迎评论