Lucas Theorem

Chef is tired of solving boring math problems by hand. One of these problems is summing up the products of elements from each k-subset of the set [n]. Here, a k-subset is a subset containing exactly k elements and [n] refers to the set which contains all integers between 1 and n (inclusive). More formally: Let’s denote this number by f(n, k). Note that f(n, 0) = 1. Since calculating f(n, k) is t