Given $$d \in \mathbb{N}_0$$ dice that each have $$f \in \mathbb{N}_0$$ faces numbered 1 to $$n$$. How many ways are there to get total sum $$s$$, where $$s$$ is the sum of all eyes on all faces when all the dice are thrown.

Assignment

Write a function throws that takes three integers $$d, f, s \in \mathbb{N}_0$$. The function must return the number of different ways to get total sum $$s$$, where $$d \in \mathbb{N}_0$$ is the number of dice, $$f \in \mathbb{N}_0$$ is the number of faces of each dye and $$s$$ is the sum of all eyes on all faces when all the dice are thrown.

Example

>>> throws(3, 6, 8)
21
>>> throws(3, 6, 12)
25
>>> throws(8, 10, 25)
318648