TopCoder problem "ProductAndSum" used in SRM 500 (Division I Level Three)



Problem Statement

    NOTE: This problem statement contains superscripts that may not display properly if viewed outside of the applet.



A positive integer is called nice if the sum of its digits is equal to S and the product of its digits is equal to 2p2 * 3p3 * 5p5 * 7p7. Return the sum of all nice integers, modulo 500,500,573.
 

Definition

    
Class:ProductAndSum
Method:getSum
Parameters:int, int, int, int, int
Returns:int
Method signature:int getSum(int p2, int p3, int p5, int p7, int S)
(be sure your method is public)
    
 

Constraints

-p2, p3, p5 and p7 will each be between 0 and 100, inclusive.
-S will be between 1 and 2,500, inclusive.
 

Examples

0)
    
2
0
0
0
4
Returns: 26
There are two nice integers: 22 and 4. Their sum is 26.
1)
    
0
0
0
0
10
Returns: 110109965
A single nice integer is 1,111,111,111.
2)
    
2
0
0
0
5
Returns: 610
41 + 14 + 221 + 212 + 122 = 610.
3)
    
1
1
1
1
10
Returns: 0
There are no nice integers in this case.
4)
    
5
5
5
5
100
Returns: 61610122

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=11345

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14429&pm=11345

Writer:

Chmel_Tolstiy

Testers:

PabloGilberto , ivan_metelsky , Smylic

Problem categories:

Brute Force, Dynamic Programming, Math