Kth Numbers

You are given a sequence $A_1, A_2, \ldots, A_N$. We want to generate a sequence $F_1, F_2, \ldots, F_N$ using the following process: - initially, $F_i = 0$ for each valid $i$. - $A$ has $2^N-1$ non-empty subsequences. For each of these subsequences (let's denote it by $S_1, S_2, \ldots, S_L$, where $L$ is the length of this subsequence), perform the following assignment: for each $i$ ($1 \le i