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

Sample Input 1

3 3
1 2 3

Sample Output 1

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 $(1+2)^3 + (1+3)^3 + (2+3)^3 = 27 + 64 + 125 = 216$.

Sample Input 2

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

Sample Output 2

90
180
360
720
1440
2880
5760
11520
23040
46080

Sample Input 3

2 5
1234 5678

Sample Output 3

6912
47775744
805306038
64822328
838460992

Be sure to print the sum modulo $998244353$.