Do Use FFT

You are given integer sequences $A$, $B$, and $C$, each of length $N$. For each $k=1,2,\ldots,N$, find the following value modulo $998244353$.

$\sum\_{1 \leq i \leq N} \left( C\_i \times \prod\_{1 \leq j \leq k} (A\_i+B\_j) \right)$

The first line contains an integer $N$ ($1 \leq N \leq 250000$).

The second line contains $N$ integers $A\_1,A\_2,\ldots,A\_N$ ($0 \leq A\_i < 998244353$).

The third line contains $N$ integers $B\_1,B\_2,\ldots,B\_N$ ($0 \leq B\_i < 998244353$).

The fourth line contains $N$ integers $C\_1,C\_2,\ldots,C\_N$ ($0 \leq C\_i < 998244353$).

For each $k=1,2,\ldots,N$, print the answer.