Score : $600$ points

Problem Statement

Given are integer sequence of length $N$, $A = (A_1, A_2, \cdots, A_N)$, and an integer $K$.

For each $X$ such that $1 \le X \le K$, find the following value:

$\left(\displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} (A_L+A_R)^X\right) \bmod 998244353$

Constraints

• All values in input are integers.
• $2 \le N \le 2 \times 10^5$
• $1 \le K \le 300$
• $1 \le A_i \le 10^8$

Input

Input is given from Standard Input in the following format:

$N$ $K$

$A_1$ $A_2$ $\cdots$ $A_N$

Output

Print $K$ lines.

The $X$-th line should contain the value $\left(\displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} (A_L+A_R)^X \right) \bmod 998244353$.

3 3
1 2 3

12
50
216

In the $1$-st line, we should print $(1+2)^1 + (1+3)^1 + (2+3)^1 = 3 + 4 + 5 = 12$.

In the $2$-nd line, we should print $(1+2)^2 + (1+3)^2 + (2+3)^2 = 9 + 16 + 25 = 50$.

In the $3$-rd line, we should print $(1+2)^3 + (1+3)^3 + (2+3)^3 = 27 + 64 + 125 = 216$.

10 10
1 1 1 1 1 1 1 1 1 1

90
180
360
720
1440
2880
5760
11520
23040
46080

2 5
1234 5678

6912
47775744
805306038
64822328
838460992

Be sure to print the sum modulo $998244353$.