AtCoder Regular Contest 102
翻译中…
Problem Statement
翻译中…
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 $998244353$:
翻译中…
- The number of combinations of
$N$sides shown by the dice such that the sum of no two different sides is$i$.
翻译中…
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.
翻译中…
Constraints
翻译中…
$1 \leq K \leq 2000$$2 \leq N \leq 2000$$K$and$N$are integers.
翻译中…
Input
翻译中…
Input is given from Standard Input in the following format:
翻译中…
K N翻译中…
Output
翻译中…
Print $2K-1$ integers. The $t$-th of them $(1\leq t\leq 2K-1)$ should be the answer for $i=t+1$.
翻译中…
样例
Input #1
3 3
Output #1
7
7
4
7
7
- For $i=2$, the combinations $(1,2,2),(1,2,3),(1,3,3),(2,2,2),(2,2,3),(2,3,3),(3,3,3)$ satisfy the condition, so the answer is $7$.
- For $i=3$, the combinations $(1,1,1),(1,1,3),(1,3,3),(2,2,2),(2,2,3),(2,3,3),(3,3,3)$ satisfy the condition, so the answer is $7$.
- For $i=4$, the combinations $(1,1,1),(1,1,2),(2,3,3),(3,3,3)$ satisfy the condition, so the answer is $4$.
Input #2
4 5
Output #2
36
36
20
20
20
36
36
Input #3
6 1000
Output #3
149393349
149393349
668669001
668669001
4000002
4000002
4000002
668669001
668669001
149393349
149393349
题目信息
题面与样例版权归 AtCoder 及出题人所有；中文翻译由 AI 生成（CI 管线），如有出入请以原文为准。