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 <cstdio>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <vector>

using namespace std;

double binom(int m,int k,double p)
{
	double x=pow(p,k)*pow(1-p,m-k);
	for(int i=0;i<k;i++)
		x*=(m-i)/(i+1.);
	return x;
}

int main()
{
	for(int n,m,L;cin>>n>>m>>L;){
		vector<double> ps(n);
		vector<int> ts(n),vs(n);
		for(int i=0;i<n;i++) cin>>ps[i]>>ts[i]>>vs[i],ps[i]/=100;
		
		vector<vector<double>> ss(n,vector<double>(m+1));
		for(int i=0;i<n;i++)
			for(int j=0;j<=m;j++)
				ss[i][j]=binom(m,j,ps[i]);
		
		vector<double> res(n);
		for(int i=0;i<n;i++)
			for(int j=0;j<=m;j++){
				double temp=1;
				for(int k=0;k<n;k++) if(k!=i){
					double win=0;
					for(int l=0;l<=m;l++)
						// l/vs[i]+j*ts[i] < l/vs[k]+l*ts[k]
						if((L+j*ts[i]*vs[i])*vs[k]<(L+l*ts[k]*vs[k])*vs[i])
							win+=ss[k][l];
					temp*=win;
				}
				res[i]+=ss[i][j]*temp;
			}
		
		for(int i=0;i<n;i++)
			printf("%.8f\n",res[i]);
	}
}