come up with a python coding to solve

Suppose we have n plates that we need to stack into exactly k non-emptypiles so that each pile contains a different number of plates. We let (,)f(n,k) denote the largest possible size of the smallest pile when this is done.

For example, there are exactly three different ways to stack 9 plates into 3 non-empty piles of different size:

1, 2, 6 1, 3, 5 2, 3, 4

Among these arrangements, the largest possible size of the smallest pile is 2, so (9,3)=2f(9,3)=2.

Find (100,4)