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}.

Examples

Input

2 2 50
30 50 1
30 50 2

Output

0.28770000
0.71230000

Input

2 1 100
100 100 10
0 100 1

Output

0.00000000
1.00000000

Input

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

Output

0.12500000
0.12500000
0.12500000

Input

2 2 50
30 0 1
30 50 2

Output

0.51000000
0.49000000

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