UVa 10922 - 2 the 9s

10922 - 2 the 9s

 * http://acm.uva.es/p/v109/10922.html

Summary
Given a number which may have many digits, determine whether it is a multiple of 9, and if it is, determine its "9-degree".

Explanation
Consider some number N, and let S be the sum of digits of N. If S is equal to 9, or if S is divisible by 9, then N is also divisible by 9. This test is fairly simple to make recursive, and the 9-degree is defined to be the depth of the recursion involved. The only problem one should or may have is the meaning of 9-degree. It's the number of times you can sum-up the digits of the sum recursively as long as sum>9.

Gotcha's

 * The 9-degree of 9 is 1, even though its sum of digits is obviously divisible by 9.

Input
999999999999999999999 9 9999999999999999999999999999998

Output
999999999999999999999 is a multiple of 9 and has 9-degree 3. 9 is a multiple of 9 and has 9-degree 1. 9999999999999999999999999999998 is not a multiple of 9.