`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`

`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.

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}`.

2 2 50 30 50 1 30 50 2

0.28770000 0.71230000

2 1 100 100 100 10 0 100 1

0.00000000 1.00000000

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

0.12500000 0.12500000 0.12500000

2 2 50 30 0 1 30 50 2

0.51000000 0.49000000

Source: ACM-ICPC Japan Alumni Group Summer Camp 2011
, Day 3, Tokyo, Japan, 2011-09-19

http://acm-icpc.aitea.net/

http://acm-icpc.aitea.net/