G. PolandBall and Many Other Ballstime limit per test6 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputPolandBall is standing in a row with Many Other Balls. More precisely, there are exactly n Balls. Balls are proud of their home land — and they want to prove that it's strong.The Balls decided to start with selecting exactly m groups of Balls, each consisting either of single Ball or two neighboring Balls. Each Ball can join no more than one group.The Balls really want to impress their Enemies. They kindly asked you to calculate number of such divisions for all m where 1 ≤ m ≤ k. Output all these values modulo 998244353, the Enemies will be impressed anyway.InputThere are exactly two numbers n and k (1 ≤ n ≤ 109, 1 ≤ k < 215), denoting the number of Balls and the maximim number of groups, respectively.OutputYou should output a sequence of k values. The i-th of them should represent the sought number of divisions into exactly i groups, according to PolandBall's rules.ExamplesInput3 3Output5 5 1 Input1 1Output1 Input5 10Output9 25 25 9 1 0 0 0 0 0 NoteIn the first sample case we can divide Balls into groups as follows: {1}, {2}, {3}, {12}, {23}.{12}{3}, {1}{23}, {1}{2}, {1}{3}, {2}{3}.{1}{2}{3}.Therefore, output is: 5 5 1.
Input3 3
Output5 5 1 
['combinatorics', 'divide and conquer', 'dp', 'fft', 'math', 'number theory', '*3200']