21268번 - Do Use FFT 다국어

문제

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

$$ \sum_{1 \leq i \leq N} \left( C_i \times \prod_{1 \leq j \leq k} (A_i+B_j) \right) $$

입력

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

The second line contains $N$ integers $A_1,A_2,\ldots,A_N$ (0ドル \leq A_i < 998244353$).

The third line contains $N$ integers $B_1,B_2,\ldots,B_N$ (0ドル \leq B_i < 998244353$).

The fourth line contains $N$ integers $C_1,C_2,\ldots,C_N$ (0ドル \leq C_i < 998244353$).

출력

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

제한

힌트