Problem: 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

Solution (in PYTHON3):

Solution:

import bisect
def nCr(n, r):
    r = min(r, n-r)
    numerator = 1
    for i in range(n, n-r, -1):
        numerator *= i
    denominator = 1
    for i in range(r, 1, -1):
        denominator *= i
    return numerator // denominator

n,m,l=map(int,input().split())
data = [[0 for i in range(m+1)]for i in range(n)]
for i in range(n):
    p,t,v=map(int,input().split())
    for j in range(m+1):
        data[i][j]=((t*j+l/v)if v!=0 else 9999999999999999, (p/100.0)**(j) * nCr(m,j) * (1-p/100.0)**(m-j))

ans=[]
for i in range(n):
    win=0
    for j in range(m+1):
        wintmp=data[i][j][1]
        for x in range(n):
            if i==x:
                continue
            tmp=0
            for a,b in data[x][bisect.bisect_right(data[x],(data[i][j][0],5)):]:
                tmp+=b
            wintmp*=tmp
        win+=wintmp
    ans.append(win)

for a in ans:
    print('%.8f'%a)