Problem Description

Given an $n$-degree polynomial $f(x)$, for each $i \in [1,m]$, compute $f(a_i)$.

Input Format

The first line contains two positive integers $n,m$, representing the degree of the polynomial and the number of points to evaluate.

The second line contains $n+1$ non-negative integers, giving the coefficients of the polynomial from low degree to high degree.

The third line contains $m$ non-negative integers, representing $a_i$.

Output Format

Output a total of $m$ lines, each containing $1$ non-negative integer.

The number on line $i$ represents $f(a_i)$.

The answer should be taken modulo $998244353$.

10 10
18 2 6 17 7 19 17 6 2 12 14
4 15 5 20 2 6 20 12 16 5

18147258
804760733
161737928
73381527
23750
973451550
73381527
525589927
842520242
161737928

Hint

Constraints: $n,m \in [1,64000]$, $a_i,[x^i]f(x) \in [0,998244352]$.

$[x^i]f(x)$ represents the coefficient of the $i$-th term of $f(x)$.

Translated by ChatGPT 5