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Given a value N, find the number of ways to make change for N cents, if we have infinite supply of each of S = { S1, S2, .. , S} valued coins. 

Example 1:

Input:
n = 4 , m = 3
S[] = {1,2,3}
Output: 4
Explanation: Four Possible ways are:
{1,1,1,1},{1,1,2},{2,2},{1,3}.


Example 2:

Input:
n = 10 , m = 4
S[] ={2,5,3,6}
Output: 5
Explanation: Five Possible ways are:
{2,2,2,2,2}, {2,2,3,3}, {2,2,6}, {2,3,5} 
and {5,5}.

 

Your Task:
You don't need to read input or print anything. Your task is to complete the function count() which accepts an array S[] its size m and n as input parameter and returns the number of ways to make change for N cents.



Expected Time Complexity: O(m*n).
Expected Auxiliary Space: O(n). 


Constraints:
1 <= n,m <= 103

 

** For More Input/Output Examples Use 'Expected Output' option **

Author: shef5


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