Mr. Beast’s Generous Giveaway

Problem Statement:

YouTube has hired Mr. Beast to host their new event to support rising content creators. As usual, to make things impressive, Jimmy (Mr. Beast) decides to give-away $M in coins.

However, Jimmy’s bank only has coins of denominations in the array F.

Determine how many ways change can be made for amount $M. There are an infinite number of coins of each denomination

Example:
M = 4
F = {10,4,1,2}
There are 4 ways to make change for M: {4}, {1,1,1,1}, {2,1,1}, {2,2}.

Constraints:

• 1 ≤ F_i ≤ 50 (1 ≤ i ≤ X)
• 1 ≤ M ≤ 250
• 1 ≤ X ≤ 50

Input Format:

• The first line contains two space-separated integers and M, X where M is the amount to be given away and X is the number of coin denominations
• The second line contains space-separated integers that describe the values of each coin type.

Output Format:

• Print a single integer representing the number of ways to make the change

Sample input:

10 4 2 5 3 6 

Sample output:

5