Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

G. PolandBall and Many Other Balls

time limit per test

6 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard 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.

Input

There are exactly two numbers *n* and *k* (1 ≤ *n* ≤ 10^{9}, 1 ≤ *k* < 2^{15}), denoting the number of Balls and the maximim number of groups, respectively.

Output

You 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.

Examples

Input

3 3

Output

5 5 1

Input

1 1

Output

1

Input

5 10

Output

9 25 25 9 1 0 0 0 0 0

Note

In 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.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/17/2018 16:11:29 (d2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|