How many ways, number N can be written as sum of M positive integers where each element is not greater than K

Question

For example, for N = 7, M = 3, K = 3, the result is

1 + 3 + 3

3 + 1 + 3

3 + 3 + 1

2 + 2 + 3

2 + 3 + 2

3 + 2 + 2

Total 6

according to the comment of JMoravitz, I tried to solve it using generating function. But is there any way to find the co-efficient of x^n more efficiently? For example, when N = 1000000000000000000, M = 11111111112, k = 90000000? I need to find no of ways mod m