
Marathon Match
N people run a marathon.
There are M resting places on the way.
For each resting place, the i-th runner takes a break with probability P_i percent.
When the i-th runner takes a break,  he gets rest for T_i time.
The i-th runner runs at constant speed V_i, and
the  distance of the marathon is L.
You are requested to compute the probability  for each runner to win the first place.
If a runner arrives at the goal with another person at the same time, they are not considered to win the first place.
Input
A dataset is given in the following format:
N M L
P_1 T_1 V_1
P_2 T_2 V_2
...
P_N T_N V_N
The first line of a dataset contains three integers N (1 \leq N \leq 100), M (0 \leq M \leq 50) and L (1 \leq L \leq 100,000).
N is the number of runners.
M is the number of resting places.
L is the  distance of the marathon.
Each of the following N lines contains three integers P_i (0 \leq P_i \leq 100), T_i (0 \leq T_i \leq 100) and V_i (0 \leq V_i \leq 100) describing the i-th runner.
P_i is the probability to take a break.
T_i is the time of resting.
V_i is the speed.
Output
For each runner, you should answer the probability of winning.
The i-th line in the output should be the probability that the i-th runner wins the marathon.
Each number in the output should not contain an error greater than 10^{-5}.
Sample Input 1
2 2 50
30 50 1
30 50 2
Output for the Sample Input 1
0.28770000
0.71230000
Sample Input 2
2 1 100
100 100 10
0 100 1
Output for the Sample Input 2
0.00000000
1.00000000
Sample Input 3
3 1 100
50 1 1
50 1 1
50 1 1
Output for the Sample Input 3
0.12500000
0.12500000
0.12500000
Sample Input 4
2 2 50
30 0 1
30 50 2
Output for the Sample Input 4
0.51000000
0.49000000
