D-Function

Dr.D is tired of making up stories, so here is the formal description of this problem : You are given a set $S = \{S_1, S_2, \ldots, S_K\}$, an integer $X$ and a sequence $A_1, A_2, \ldots, A_M$. Let's define an infinite sequence $W_1, W_2, \ldots$: for each valid $i$, $W_i = A_{((i-1) \% M) + 1}$. Then, let's define a function $F(i)$ for any non-negative integer $i$ in the following way: - $F(0)