AtCoder Regular Contest 104
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Problem Statement
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Given positive integers $N, K$ and $M$, solve the following problem for every integer $x$ between $1$ and $N$ (inclusive):
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- Find the number, modulo
$M$, of non-empty multisets containing between$0$and$K$(inclusive) instances of each of the integers$1, 2, 3 \cdots, N$such that the average of the elements is$x$.
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Constraints
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$1 \leq N, K \leq 100$$10^8 \leq M \leq 10^9 + 9$$M$is prime.- All values in input are integers.
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Input
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Input is given from Standard Input in the following format:
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N K M翻译中…
Output
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Use the following format:
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c_1
c_2
:
c_N翻译中…
Here, $c_x$ should be the number, modulo $M$, of multisets such that the average of the elements is $x$.
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样例
Input #1
3 1 998244353
Output #1
1
3
1
Consider non-empty multisets containing between $0$ and $1$ instance(s) of each of the integers between $1$ and $3$. Among them, there are:
- one multiset such that the average of the elements is $k = 1$: $\{1\}$;
- three multisets such that the average of the elements is $k = 2$: $\{2\}, \{1, 3\}, \{1, 2, 3\}$;
- one multiset such that the average of the elements is $k = 3$: $\{3\}$.
Input #2
1 2 1000000007
Output #2
2
Consider non-empty multisets containing between $0$ and $2$ instances of each of the integers between $1$ and $1$. Among them, there are:
- two multisets such that the average of the elements is $k = 1$: $\{1\}, \{1, 1\}$.
Input #3
10 8 861271909
Output #3
8
602
81827
4054238
41331779
41331779
4054238
81827
602
8
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。