9968: ABC315 —— Ex - Typical Convolution Problem
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Description
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 $998244353$.
- $F_0 = 1$
- $F_n = A_n\displaystyle\sum_{i+j<n}F_iF_j$ $(1 \leq n \leq N)$
Find $F_1, \ldots , F_N$ modulo $998244353$.
Input
The input is given from Standard Input in the following format:
```
$N$
$A_1$ $A_2$ $\ldots$ $A_N$
```
```
$N$
$A_1$ $A_2$ $\ldots$ $A_N$
```
Output
Print $F_1, \ldots , F_N$ modulo $998244353$ in this order, with spaces in between.
Constraints
- $1 \leq N \leq 2 \times 10^5$
- $0 \leq A_i < 998244353$
- All input values are integers.
- $0 \leq A_i < 998244353$
- All input values are integers.
Sample 1 Input
5
1 2 3 4 5
Sample 1 Output
1 6 48 496 6240
Sample 2 Input
3
12345 678901 2345678
Sample 2 Output
12345 790834943 85679169