3753 . [模板題] Convolution on the Multiplicative Monoid of $\mathbb{Z} / P\mathbb{Z}$

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User's AC Ratio

100.0% (1/1)

Submission's AC Ratio

100.0% (1/1)

Tags

library-checker template

Description

Given a prime $P$ and integer sequences $a_ 0, a_ 1, ..., a_ {P - 1}$ and $b_ 0, b_ 1, ..., b_ {P - 1}$. Calculate an integer sequence $c_ 0, c_ 1, ..., c_ {P - 1}$ as follows:

$$c_ k = \sum_ {i \times j \equiv k \pmod{P}} a_ i b_ j \bmod 998244353$$

Input Format

$P$
$a_ 0$ $a_ 1$ ... $a_ {P - 1}$
$b_ 0$ $b_ 1$ ... $b_ {P - 1}$

Output Format

$c_ 0$ $c_ 1$ ... $c_ {P - 1}$

Sample Input 1

5
9 7 5 3 1
8 6 4 2 0

Sample Output 1

308 64 60 36 32

Sample Input 2

2
0 998244352
0 998244352

Sample Output 2

0 1

Hints

  • $2 \leq P \leq 2^ {19}$
  • $P$ is a prime
  • $0 \leq a_ i, b_ i < 998244353$

Problem Source

library checker: mul_modp_convolution

Subtasks

No. Testdata Range Score

Testdata and Limits

No. Time Limit (ms) Memory Limit (VSS, KiB) Output Limit (KiB) Subtasks
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