You have types of coins available in infinite quantities where the value of each coin is given in the array . Can you determine the number of ways of making change for units using the given types of coins? For example, if , and , we can make change for units in three ways: , , and .
Given , , and , print the number of ways to make change for units using any number of coins having the values given in .
The first line contains two space-separated integers describing the respective values of and .
The second line contains space-separated integers describing the respective values of (the list of distinct coins available in infinite amounts).
Each is guaranteed to be distinct.
Solve overlapping subproblems using Dynamic Programming (DP):
You can solve this problem recursively but will not pass all the test cases without optimizing to eliminate the overlapping subproblems. Think of a way to store and reference previously computed solutions to avoid solving the same subproblem multiple times.
Consider the degenerate cases:
How many ways can you make change for cents?
How many ways can you make change for cents if you have no coins?
If you're having trouble defining your solutions store, then think about it in terms of the base case .
The answer may be larger than a -bit integer.
Print a long integer denoting the number of ways we can get a sum of from the given infinite supply of types of coins.
Sample Input 0
4 31 2 3
Sample Output 0
There are four ways to make change for using coins with values given by :
Thus, we print as our answer.
Sample Input 1
10 42 5 3 6
Sample Output 1
There are five ways to make change for units using coins with values given by :