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<iostream>
#include<cstdio>
#include<cmath>
using namespace std;

int main(){
  int n,m,l;
  double p;
  int t,v;
  double time[100][51],prob[100][51];

  cin >> n >> m >> l;
  for(int i=0;i<n;i++){
    cin >> p >> t >> v;
    p /= 100;
    for(int j=0;j<=m;j++)time[i][j] = (double)l/v + t*j;
  
    if(abs(p-1.0)<1e-10){
      for(int j=0;j<m;j++)prob[i][j] = 0.0;
      prob[i][m] = 1.0;
    }else{
      prob[i][0] = pow(1-p,m);
      for(int j=1;j<=m;j++){
	prob[i][j] = ( prob[i][j-1] * p * (m-j+1) ) / ( (1-p)*j );
      }
    }
  }
  
  for(int i=0;i<n;i++){
    double ans = 0.0;
    for(int j=0;j<=m;j++){
      double tmp = 1.0;
      for(int k=0;k<n;k++){
	if(k!=i){
	  double hoge = 0.0;
	  for(int l=m;l>=0;l--){
	    if(time[k][l] > time[i][j]){
	      hoge += prob[k][l];
	    }else break;
	  }
	    tmp *= hoge;
	}
      }
      ans += tmp*prob[i][j];
    }
    printf("%.8lf\n",ans);
  }
}