Problem Background

On May 28, 2021, the Tokamak device "YiST" of the Yi Kingdom successfully conducted its first experiment, operating at $1.2 \times 10^8 \ ^\circ\text{C}$ for $102\text{ s}$.

In the year 3021, the Interstellar Federation of humanity began a new round of experiments—the extraction of vacuum zero-point energy.

A vacuum zero-point energy extraction experiment can be abstracted as the following process:

There are $n$ intervals $[l_i, r_i]$ generated randomly according to the following rules: * For each $i$, first take independent uniform random variables $x_i, y_i \in [0, 1]$, then let $l_i = \min(x_i, y_i)$ and $r_i = \max(x_i, y_i)$.

If there exists an $x \in [0, 1]$ such that at least $k$ intervals cover $x$, the energy threshold is breached, and the experiment is considered a success.

Yi Ai wants to know, for each $n$ ($k \le n \le N$), what is the probability that the experiment is successful when there are $n$ intervals?

You only need to output the answer modulo $998244353$.

Input

Input two positive integers $N, k$.

Output

Output $N - k + 1$ lines, each containing an integer. The $i$-th line represents the answer when generating $n = k + i - 1$ intervals.

Examples

Input 1

4 2

Output 1

665496236
133099248
874652196

Input 2

10 5

Output 2

649651087
469592582
90638682
971355617
213732434
682398780

Input 3

5000 4990

Output 3

433547646
604946601
315883076
866829944
796432253
375436914
90833037
455045447
570901064
289574480
958621891

Constraints

• For the first $10\%$ of the data, $N \le 10$.
• For the first $30\%$ of the data, $N \le 10^3$.
• For another $20\%$ of the data, $k \le 10^2, N \le 10^5$.
• For the first $70\%$ of the data, $k \le 5 \times 10^4$.
• For the first $90\%$ of the data, $N \le 2 \times 10^5$.
• For $100\%$ of the data, $2 \le k \le N \le 5 \times 10^5$.