Score : $650$ points

问题描述

你已给定一个序列 $(A_1, A_2, \ldots , A_N)$。让我们通过以下公式定义一个序列 $(F_0, F_1, \ldots , F_N)$。

• $F_0 = 1$
• $F_n = A_n\displaystyle\sum_{i+j<n}F_iF_j$ $(1 \leq n \leq N)$

求 $F_1, \ldots , F_N$ 对于模数 $998244353$ 的结果。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given a sequence $(A_1, A_2, \ldots , A_N)$. Let us define a sequence $(F_0, F_1, \ldots , F_N)$ by the following formulae.

• $F_0 = 1$
• $F_n = A_n\displaystyle\sum_{i+j<n}F_iF_j$ $(1 \leq n \leq N)$

Find $F_1, \ldots , F_N$ modulo $998244353$.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq A_i < 998244353$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\ldots$ $A_N$

Output

Print $F_1, \ldots , F_N$ modulo $998244353$ in this order, with spaces in between.

Sample Input 1

5
1 2 3 4 5

Sample Output 1

1 6 48 496 6240

$F_1 = A_1F_0F_0 = 1$. $F_2 = A_2(F_0F_0+F_0F_1+F_1F_0) = 6$. Similarly, we find $F_3 = 48, F_4 = 496, F_5 = 6240$.

Sample Input 2

3
12345 678901 2345678

Sample Output 2

12345 790834943 85679169

update @ 2024/3/10 09:01:27