DigitFiller | Topcoder Archive

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

```
"8X"
```
```
9
```
```
Returns: 1
```
Since the objects are divided evenly into 9 piles, 81 is the only possible solution.
```
"1XX"
```
```
10
```
```
Returns: 10
```
Here there are 10 possible values k could have been.
```
"14"
```
```
7
```
```
Returns: 1
```
None of the digits are missing.
```
"9999999999999X"
```
```
3
```
```
Returns: 4
```
```
"23X34XX24XX34X"
```
```
17
```
```
Returns: 58823
```

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