Game of Death

题号：NC225902
时间限制：C/C++/Rust/Pascal 2秒，其他语言4秒
空间限制：C/C++/Rust/Pascal 1024 M，其他语言2048 M
64bit IO Format: %lld

题目描述

There are $n$ players. Each player chooses exactly one player except himself with the same probability, and then every player shoots the player he chooses simultaneously. Each shot hits the chosen player with probability $p$ . All choices and hits are independent. A player dies if and only if hit by at least one shot. For each $k=0,1,\cdots,n$ , find the probability $p_k$ exactly $k$ player alive.

输入描述:

The only line contains three integers  ,  , where  is the number of players and  is the probability of hit for each shot.

输出描述:

Output  lines. In the -th line, output one integer indicating  module 998244353.

Formally, it can be proved that  is a rational number and it can be represented by  where the greatest common divisor of  and  is . You should output one integer  such that .

示例1

输入

复制

2 1 1

输出

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1
0
0

示例2

输入

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3 1 1

输出

复制

示例3

输入

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2 1 2

输出

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748683265
499122177
748683265

示例4

输入

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3 1 3

输出

复制

备注:

For the first example, .

For the second example, .

For the third example, .

For the fourth example, .