Goal
Given a non-negative amount N and a set of S coins of positive values Vi, return the number of ways to reach the required amount using the coins.
NB : You have an unlimited number of each coin at your disposal.
For example, given N = 10, S = 2 and the set of values V1 = {1, 5} , you should return 3. Indeed, there are 3 ways to sum coins of values {1, 5} up to 10 : 1*10, 5*2 and 1*5 + 5*1.
Input
Line 1 : A non-negative integer N for the target amount.
Line 2 : A positive integer S for the number of possible values coins.
Line 3 : S space-separated non-negative integer Vi for the value of the i-th coin.
Output
An integer representing the number of ways to sum the coins up to N (0 if there is no way to reach the target amount).
Constraints
0 <= N <= 2000
0 < S <= 10
0 < Vi <= 500
