Problem Statement

You have k objects divided evenly into num piles. Unfortunately, some of the digits of k may have been erased (replaced with 'X's in the input). Return the number of possible values that k could have been.

Definition

 Class: DigitFiller Method: howMany Parameters: String, int Returns: long Method signature: long howMany(String k, int num) (be sure your method is public)

Constraints

-k will contain between 2 and 18 characters inclusive.
-Each character in k will be a digit ('0'-'9') or 'X'.
-Character 0 of k will be a positive digit ('1'-'9').
-num will be between 1 and 10000 inclusive.
-The return value will be at least 1.

Examples

0)

 `"8X"` `9`
`Returns: 1`
 Since the objects are divided evenly into 9 piles, 81 is the only possible solution.
1)

 `"1XX"` `10`
`Returns: 10`
 Here there are 10 possible values k could have been.
2)

 `"14"` `7`
`Returns: 1`
 None of the digits are missing.
3)

 `"9999999999999X"` `3`
`Returns: 4`
4)

 `"23X34XX24XX34X"` `17`
`Returns: 58823`

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=4662

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=9903&pm=4662