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 CPP):

Solution:
#include "bits/stdc++.h"
#include<unordered_map>
#pragma warning(disable:4996)
using namespace std;

const int My_Inf=2147483647;
const long long int My_LInf=9223372036854775807;

double dfact(const int a) {
	assert(a >= 0);
	if (a == 0)return 1;
	return a*dfact(a - 1);
}
double dcomb(const int a, const int b) {
	return (dfact(a) / dfact(b)) / dfact(a-b);
}
double eps = 1e-9;

int main() {
	int N, M, L; cin >> N >> M >> L;
	vector<map<double, double>>mps,ruisekimps;
	for (int i = 0; i < N; ++i) {
		double P,T,V; cin >> P >> T >> V;
		P /= 100;
		map<double, double>mp;
		if (T < eps) {
			mp[L / V] = 1;
		}
		else {
			for (int rest = 0; rest <= M; ++rest) {
				mp[L / V + T*rest] = pow(P, rest)*pow(1 - P, M - rest)*dcomb(M, rest);
			}
		}
		
		mps.push_back(mp);
	}
	for (int rn = 0; rn < N; ++rn) {
		map<double, double>mp;
		double nowprob = 0;
		mp[0] = 0;
		
		for (auto prob : mps[rn]) {
			nowprob += prob.second;
			mp[prob.first] = nowprob;
		}
		mp[1e18] = 1;
		ruisekimps.push_back(mp);
	}
	for (int rn = 0; rn < N; ++rn) {
		double ans = 0;
		for(auto i:mps[rn]){
			double atime = i.first;
			double prob = i.second;
			for (int ob = 0; ob < N; ++ob) {
				if (rn == ob)continue;
				
				auto it(ruisekimps[ob].lower_bound(atime + eps));
				prob *= (1-prev(it)->second);
			}
			ans += prob;
		}
		cout <<setprecision(22)<<fixed<< ans << endl;
	}
	return 0;
}