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Time Limit: 1.5 s Memory Limit: 1024 MB Total points: 100

#619. 多项式求逆

الإحصائيات

题目描述

给定多项式 $A(z)=\sum^{n-1}_{i=0} a_ix^i$,求 $A^{-1}(z) \bmod {x^n} = \sum^{n-1}_{i=0} c_iz^n$

输入格式

输入的第一行包含一个整数 $n$。

接下来一行,包含 $n$ 个整数 $a_0,a_1,\cdots,a_{n-1}$。

输出格式

输出一行 $n$ 个整数,表示 $c_0,c_1,\cdots,c_{n-1}$。

样例数据

样例输入

8
1 9 2 6 0 8 1 7

样例输出

1 998244344 79 998243654 6187 998189586 484794 993952989

子任务

对于所有数据,$1 \leq n \leq 10^6$,$0 \le a_i < 998\,244\,353$,$a_0 \ne 0$。

测试点 $n$
$1$ $100$
$2$ $5 \times 10^3$
$3$ $3 \times 10^4$
$4$ $10^5$
$5$ $10^6$

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