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문제

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 Pi percent. When the i-th runner takes a break, he gets rest for Ti time.

The i-th runner runs at constant speed Vi, 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.

입력

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 Pi (0≤Pi≤100), Ti (0≤Ti≤100) and Vi (0≤Vi≤100) describing the i-th runner. Pi is the probability to take a break. Ti is the time of resting. Vi is the speed.

출력

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.

예제 입력 1

2 2 50
30 50 1
30 50 2

예제 출력 1

0.28770000
0.71230000

예제 입력 2

2 1 100
100 100 10
0 100 1

예제 출력 2

0.00000000
1.00000000

예제 입력 3

3 1 100
50 1 1
50 1 1
50 1 1

예제 출력 3

0.12500000
0.12500000
0.12500000

예제 입력 4

2 2 50
30 0 1
30 50 2

예제 출력 4

0.51000000
0.49000000