### Problem Statement

Given a string of digits, find the minimum number of additions required for the string to equal some target number. Each addition is the equivalent of inserting a plus sign somewhere into the string of digits. After all plus signs are inserted, evaluate the sum as usual. For example, consider the string "12" (quotes for clarity). With zero additions, we can achieve the number 12. If we insert one plus sign into the string, we get "1+2", which evaluates to 3. So, in that case, given "12", a minimum of 1 addition is required to get the number 3. As another example, consider "303" and a target sum of 6. The best strategy is not "3+0+3", but "3+03". You can do this because leading zeros do not change the result.

Write a class QuickSums that contains the method minSums, which takes a String numbers and an int sum.  The method should calculate and return the minimum number of additions required to create an expression from numbers that evaluates to sum.  If this is impossible, return -1.

### Definition

 Class: QuickSums Method: minSums Parameters: String, int Returns: int Method signature: int minSums(String numbers, int sum) (be sure your method is public)

### Constraints

-numbers will contain between 1 and 10 characters, inclusive.
-Each character in numbers will be a digit.
-sum will be between 0 and 100, inclusive.

### Examples

0)

 `"99999"` `45`
`Returns: 4`
 In this case, the only way to achieve 45 is to add 9+9+9+9+9. This requires 4 additions.
1)

 `"1110"` `3`
`Returns: 3`
 Be careful with zeros. 1+1+1+0=3 and requires 3 additions.
2)

 `"0123456789"` `45`
`Returns: 8`
3)

 `"99999"` `100`
`Returns: -1`
4)

 `"382834"` `100`
`Returns: 2`
 There are 3 ways to get 100. They are 38+28+34, 3+8+2+83+4 and 3+82+8+3+4. The minimum required is 2.
5)

 `"9230560001"` `71`
`Returns: 4`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=2829

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=5072&pm=2829

ValD

#### Testers:

lbackstrom , brett1479

#### Problem categories:

Dynamic Programming