Hi, is there any efficient techniques to do the following summation ?

Given a finite set $A$ containing $n$ integers $A=(x_1,x_2,…,x_n)$, where $x_i$ is an integer. Now there are $n$ subsets of $A$, denoted by $A_1, A_2, ... , A_n$. We want to calculate the summation for each subset, i.e., $b_i=\sum_{x_j \in A_i} x_j$.

Are there some efficient techniques to compute all the values of $b_1,..., b_n$ ?