22507번 - Marathon Match 스페셜 저지다국어

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.

A dataset is given in the following format:

N M L
P1 T1 V1
P2 T2 V2
…
PN TN VN

The first line of a dataset contains three integers N (1≤N≤100), M (0≤M≤50) and L (1≤L≤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≤P_i≤100), T_i (0≤T_i≤100) and V_i (0≤V_i≤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.

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.