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   Problem Statement  

 Problem Statement for P8XCoinChange

Problem Statement

    

The currency system in the Exponential Kingdom consists of various types of coins. The coin denominations follow these simple rules:

  • Each denomination is a positive integer.
  • There is a coin type with denomination 1.
  • For each pair of different coin types, the denomination of one coin type divides the denomination of the other one.

You are given a long[] values containing all the available denominations in ascending order. You are also given a long coins_sum. You want to pick a set of coins such that the sum of their values is exactly equal to coins_sum. Your method must count the number of ways in which such a set can be chosen. Since the answer may be very big, return it modulo 1,000,003 (10^6 + 3).

 

Definition

    
Class:P8XCoinChange
Method:solve
Parameters:long, long[]
Returns:int
Method signature:int solve(long coins_sum, long[] values)
(be sure your method is public)
    
 

Notes

-Let A and B be two sets of coins. They are considered different if and only if there exists a denomination X such that the numbers of coins worth X in A and in B differ.
 

Constraints

-coins_sum will be between 1 and 10^18, inclusive.
-values will contain between 1 and 40 elements, inclusive.
-Each element of values will be between 1 and 10^18, inclusive.
-values will be sorted in strictly ascending order. Note that this also implies that all the elements of values will be distinct.
-For each pair of different elements in values, the smaller one will be a divisor of the larger one.
-values[0] will be 1.
 

Examples

0)
    
4
{1, 3}
Returns: 2
The two sets of coins with sum 4 are:
{1, 1, 1, 1}
{1, 3}
1)
    
4
{1, 2, 4}
Returns: 4
The only possible set of coins that sums to 4 are:
{1, 1, 1, 1}
{1, 1, 2}
{2, 2}
{4}
2)
    
3
{1, 5}
Returns: 1
3)
    
11
{1, 2, 6}
Returns: 9
4)
    
1000000000000000000
{1, 1000000000, 1000000000000000000}
Returns: 997005
There are exactly 1,000,000,002 possible sets, hence you should return 1,000,000,002 modulo 1,000,003 which is equal to 997,005.
5)
    
961320341778342848
{1,2,10,30,150,300,1200,2400,4800,14400,
28800,57600,288000,576000,2304000,9216000,
18432000,73728000,221184000,663552000,
1327104000,5308416000,31850496000,
95551488000,191102976000,764411904000,
1528823808000,6115295232000,18345885696000,
36691771392000,73383542784000,220150628352000,
440301256704000,1320903770112000,3962711310336000,
15850845241344000,31701690482688000,95105071448064000,
475525357240320000,951050714480640000}
Returns: 245264
6)
    
1000000000000000000
{1, 2}
Returns: 499989

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This problem was used for:
       Single Round Match 527 Round 1 - Division I, Level Three