P15729 [JAG 2024 Summer Camp #2] Add Add Add

You are given two sequences of positive integers of length $N$, $(A_1, A_2, \ldots, A_N)$ and $(B_1, B_2, \ldots, B_N)$. For $k = 2, 3, \ldots, 2N$, compute the value of $\sum_{i+j \leq k} (A_i + B_j)$, that is, the sum of $(A_i + B_j)$ for all indices $(i, j)$ such that $i + j \leq k$ and $1 \leq i, j \leq N$.

The input is given in the following format: $$ \begin{aligned} &N \\ &A_1 \ A_2 \ \ldots \ A_N \\ &B_1 \ B_2 \ \ldots \ B_N \end{aligned} $$ - $1 \leq N \leq 200,000$ - $1 \leq A_i, B_i \leq 10^6$ ($1 \leq i \leq N$) - All input values are integers.

Output $2N - 1$ lines. On the $i$-th line ($1 \leq i \leq 2N - 1$), output the answer for the case where $k = i + 1$.