3783 . [模板題] Pow of Formal Power Series
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Description
You are given a formal power series $f(x) = \sum_ {i=0}^ {N-1} a_ i x^ i \in \mathbb{F}_ {998244353}[[x]]$ and a non-negative integer $M$.
Calculate the first $N$ terms of $(f(x))^ M = \sum_ {i=0}^ {\infty} b_ i x^ i$.
Input Format
$N$ $M$
$a_ 0$ $a_ 1$ $\cdots$ $a_ {N-1}$
Output Format
$b_ 0$ $b_ 1$ $\cdots$ $b_ {N - 1}$
Sample Input 1
4 3 0 0 9 12
Sample Output 1
0 0 0 0
Sample Input 2
2 2 1 1
Sample Output 2
1 2
Sample Input 3
2 0 0 0
Sample Output 3
1 0
Hints
- $1 \leq N \leq 5 \times 10^ {5}$
- $0 \leq M \leq 10^ {18}$
- $0 \leq a_ i < 998244353$
Problem Source
Subtasks
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