Problem Description

Given the $n + 1$ point values $f(0), f(1) \dots f(n)$ of a polynomial of degree at most $n$, and a positive integer $m$, find $f(m), f(m + 1) \dots f(m + n)$.

The answer should be taken modulo $998244353$.

Input Format

The first line contains two positive integers $n, m$, with the meanings as described above.
The second line contains $n + 1$ integers, representing $f(0), f(1) \dots f(n)$.

Output Format

Output one line with $n + 1$ integers, representing $f(m), f(m + 1) \dots f(m + n)$.

5 6
1 1 4 5 1 4

54 232 673 1579 3232 6007

Hint

Constraints
For $100\%$ of the testdata:
$1 \le n \le 160000$, $n < m \le 10^8$, $0 \le f(i) < 998244353$.

Translated by ChatGPT 5