MZL's game

Problem Description

MZL has $n$ cute boys.They are playing a game♂.The game will run in turn First,System choose an alive player $x$ randomly.Player $x$ will be out of the game. Then player x will attack all alive players in the game When a player is attacked,$1-p$ is the probability of he still lives,$p$ is the probability of he dies Now mzl wants to know：the probability of one player be out of the game and be attacked $k$ times You need to print the probability mod 258280327 for every k from 0 to n-1 According to Fermat Theory,$\frac{x}{y}$ mod 258280327=x*$(y^{258280325})$ mod 258280327 $p$ will be given in a special way

Input

The first line of the input contains a single number $T$, the number of test cases. Next $T$ lines, each line contains three integer $n$,$x$,$y$.$p=\frac{x}{y}$ $T\leq 5$, $n\leq 2*10^3$ $0 \leq x \leq 10^9$ $x+1 \leq y \leq 10^9$. It is guaranteed that y and 258280327 are coprime.

Output

$T$ lines, every line n numbers: the ans from 0 to n-1

Sample Input

2
3 33 100
9 23 233

Sample Output

172186885 210128265 223268793
229582513 70878931 75916746 175250440 21435537 57513225 236405985 111165243 115953819

Hint

for case 1: The probability of you live and not be attacked is 1/3 The probability of you live and be attacked for one time is: (2/3)(0.330.67+0.670.67(1/2))=8911/30000

Author

SXYZ

Source

2015 Multi-University Training Contest 5