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 math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**13
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


nm = {}
def nCr(n, b):
    if b > n - b:
        b = n - b
    key = (n,b)
    if key in nm:
        return nm[key]
    r = 1
    for k in range(n, n-b, -1):
        r = r * k
    d = 1
    for k in range(1, b+1):
        d = d * k
    nm[key] = r / d
    return nm[key]


def main():
    rr = []

    n,m,l = LI()
    ps = [LI() for _ in range(n)]
    ts = []
    rs = []
    us = []

    for p,t,v in ps:
        if v == 0:
            ts.append(0)
            rs.append(0)
            us.append(0)
            continue
        p /= 100
        u = l / v
        ti = []
        ri = []
        for i in range(m+1):
            ti.append(u+t*i)
            k = pow(1-p, m-i) * pow(p, i) * nCr(m, i)
            ri.append(k)
        ts.append(ti)
        rs.append(ri)
        ui = ri[:]
        for i in range(1,m+1):
            ui[i] += ui[i-1]
        us.append(ui)

    for i in range(n):
        r = 0
        if ts[i] == 0:
            rr.append(r)
            continue
        for j in range(m+1):
            tr = rs[i][j]
            tt = ts[i][j] + 1.0 / 10**10
            for k in range(n):
                if i == k or ts[k] == 0:
                    continue
                bi = bisect.bisect_left(ts[k], tt)
                if bi > 0:
                    tr *= 1 - us[k][bi-1]
            r += tr
        rr.append('{:.9f}'.format(r))

    return '\n'.join(map(str,rr))


print(main())