H. HW0.514
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

Boluteshih and 2qbingquan are preparing the problems for Homework 0.514. Boluteshih selected $$$N$$$ problems, while 2qbingquan selected $$$M$$$ problems for the homework.

To make it harder to identify which problems were prepared by whom, Boluteshih wrote a Python script to shuffle the order of these problems randomly. As a coincidence, Boluteshih discovered that after shuffling, the problems chosen by 2qbingquan formed a contiguous subarray within the shuffled list.

Just out of curiosity, you are asked to answer the probability that the problems chosen by 2qbingquan just formed $$$k$$$ contiguous subarray within the shuffled list, for each $$$k$$$ from $$$1$$$ to $$$M$$$. All $$$(N + M)!$$$ permutations of the $$$N + M$$$ problems are considered equiprobable during the shuffle.

As usual, you are asked to output the answer modulo $$$998244353$$$ (see output section).

Input

The input only contains one line with two space-separated integers $$$N, M$$$.

  • $$$1 \leq N, M \leq 10^6$$$.
Output

Print $$$M$$$ space-separated integers, where the $$$i$$$-th is the probability of that the problems chosen by 2qbingquan just formed $$$k$$$ contiguous subarray, modulo $$$998244353$$$.

For each $$$k$$$, it can be shown that the probability is in the form of $$$\frac{P}{Q}$$$ where $$$P$$$ and $$$Q$$$ are non-negative integers and $$$Q \neq 0, \mathrm{gcd}(P, Q) = 1$$$. By modulo $$$998244353$$$ it means $$$P\cdot Q^{-1} \pmod{998244353}$$$, which should be an integer in $$$[0, 998244353)$$$.

Examples
Input
1 2
Output
665496236 332748118
Input
2 5
Output
855638017 427819009 713031681 0 0
Input
37 9
Output
773088076 617179006 965409427 423633148 606148699 470916699 791168354 947239560 394683150