Write a function, counting_change, that takes in an amount and a list of coins. The function should return the number of different ways it is possible to make change for the given amount using the coins.
You may reuse a coin as many times as necessary.
For example,
ounting_change(4, [1,2,3]) -> 4
There are four different ways to make an amount of 4:
1. 1 + 1 + 1 + 1
2. 1 + 1 + 2
3. 1 + 3
4. 2 + 2
counting_change(4, [1, 2, 3]) # -> 4counting_change(8, [1, 2, 3]) # -> 10counting_change(24, [5, 7, 3]) # -> 5counting_change(13, [2, 6, 12, 10]) # -> 0counting_change(512, [1, 5, 10, 25]) # -> 20119counting_change(1000, [1, 5, 10, 25]) # -> 142511counting_change(240, [1, 2, 3, 4, 5, 6, 7, 8, 9]) # -> 1525987916