Score : 700 points
Takahashi throws N dice, each having K sides with all integers from 1 to K. The dice are NOT pairwise distinguishable. For each i=2,3,...,2K, find the following value modulo 998244353:
Note that the dice are NOT distinguishable, that is, two combinations are considered different when there exists an integer k such that the number of dice showing k is different in those two.
Input is given from Standard Input in the following format:
K N
Print 2K-1 integers. The t-th of them (1\leq t\leq 2K-1) should be the answer for i=t+1.
3 3
7 7 4 7 7
4 5
36 36 20 20 20 36 36
6 1000
149393349 149393349 668669001 668669001 4000002 4000002 4000002 668669001 668669001 149393349 149393349