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 <cstring>
#include <cmath>
#include <algorithm>
using namespace std;
int n,m;
double l;
int t[101];
double pp[101][55];
double psum[101][55];
double p[101],v[101];
double tt[101][55];
double win[101];
double comb[101][101];

int main(void){
	comb[0][0]=1;
	for(int i=1;i<=100;i++){
		comb[i][0]=1;
		comb[i][i]=1;
		for(int j=1;j<i;j++){
			comb[i][j]=comb[i-1][j]+comb[i-1][j-1];
		}
	}
	scanf("%d %d %lf",&n,&m,&l);
	for(int i=0;i<n;i++){
		scanf("%lf %d %lf",&p[i],&t[i],&v[i]);
		p[i]=p[i]/100.0;
	}
	for(int j=0;j<n;j++){
		for(int k=0;k<=m;k++){
			pp[j][k]=comb[m][k];
			for(int l=0;l<k;l++){
				pp[j][k]*=p[j];
			}
			for(int l=0;l<m-k;l++){
				pp[j][k]*=(1.0-p[j]);
			}
		}
	}
	for(int i=0;i<n;i++){
		for(int j=0;j<=m;j++){
			psum[i][j+1]=psum[i][j]+pp[i][j];
		}
	}
	for(int i=0;i<n;i++){
		if(v[i]==0.0){
			for(int j=0;j<=m+1;j++){
				tt[i][j]=1000000000.0;
			}
			continue;
		}
		tt[i][0]=l/v[i];
		for(int j=1;j<=m;j++){
			tt[i][j]=tt[i][j-1]+t[i];
		}
		tt[i][m+1]=1000000000.0;
	}
	for(int i=0;i<n;i++){
		if(v[i]==0.0)continue;
		for(int l=0;l<=m;l++){
			double wp=pp[i][l];
			for(int k=0;k<n;k++){
				if(k==i)continue;
				if(v[k]==0.0)continue;
				int uk=upper_bound(tt[k],tt[k]+m+2,tt[i][l])-tt[k];
				wp*=(1.0-psum[k][uk]);
				//printf("%lf %lf %f\n",tt[i][l],tt[k][uk],psum[k][uk]);
			}
			win[i]+=wp;
		}
	}
	for(int i=0;i<n;i++){
		printf("%.8f\n",win[i]);
	}
	return 0;
}