Combinatorics Problem

Recall that the binomial coefficient $$$\binom{x}{y}$$$ is calculated as follows ($$$x$$$ and $$$y$$$ are non-negative integers):

• if $$$x < y$$$, then $$$\binom{x}{y} = 0$$$;
• otherwise, $$$\binom{x}{y} = \frac{x!}{y! \cdot (x-y)!}$$$.

You are given an array $$$a_1, a_2, \dots, a_n$$$ and an integer $$$k$$$. You have to calculate a new array $$$b_1, b_2, \dots, b_n$$$, where

• $$$b_1 = (\binom{1}{k} \cdot a_1) \bmod 998244353$$$;
• $$$b_2 = (\binom{2}{k} \cdot a_1 + \binom{1}{k} \cdot a_2) \bmod 998244353$$$;
• $$$b_3 = (\binom{3}{k} \cdot a_1 + \binom{2}{k} \cdot a_2 + \binom{1}{k} \cdot a_3) \bmod 998244353$$$, and so on.

Formally, $$$b_i = (\sum\limits_{j=1}^{i} \binom{i - j + 1}{k} \cdot a_j) \bmod 998244353$$$.

Note that the array is given in a modified way, and you have to output it in a modified way as well.