Problem:
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

Solution in Python (judge verdict: Accepted)

#!/usr/bin/env python

from collections import deque
import itertools as it
import sys

sys.setrecursionlimit(1000000)

N, M, L = map(int, raw_input().split())

def fact(n):
    if n <= 1:
        return 1
    return fact(n - 1) * n
MC = []
for i in range(M + 1):
    MC.append(fact(M) / fact(i) / fact(M - i))

p_lst = []
P_val = []
P_sum = []

for i in range(N):
    P, T, V = map(int, raw_input().split())
    p_lst.append((T, V))
    PP = []
    for k in range(M + 1):
        PP.append(float(MC[k] * (P ** k) * ((100 - P) ** (M - k))) / 100 ** M)
    P_val.append(list(PP))
    for k in range(M, 0, -1):
        PP[k - 1] += PP[k]
    P_sum.append(PP)

def comp(p1, p2, k1, k2):
    T1, V1 = p1
    T2, V2 = p2
    return L * (V2 - V1) < V1 * V2 * (k2 * T2 - k1 * T1)

for i in range(N):
    ans = 0
    index_lst = [0 for j in range(N)]
    for k1 in range(M + 1):
        ret = P_val[i][k1]
        for j in range(N):
            if i == j:
                continue
            while True:
                k2 = index_lst[j]
                if k2 > M:
                    ret *= 0
                    break
                if comp(p_lst[i], p_lst[j], k1, k2):
                    ret *= P_sum[j][k2]
                    break
                index_lst[j] += 1
        ans += ret
    print '%.10f' % ans