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

using namespace std;

const int N = 100;
const int M = 51;
const double EPS = 1e-9;

int n, m, L, t[N], v[N];
double p[N], C[M+1][M+1], ps[N][N], s_ps[N][N], ts[N][N];

int main(){
  for(int i=0;i<=M;i++) C[i][0] = 1.0;
  for(int i=1;i<=M;i++) for(int j=1;j<=i;j++) C[i][j] = C[i-1][j-1] + C[i-1][j];
  cin >> n >> m >> L;
  for(int i=0;i<n;i++) cin >> p[i] >> t[i] >> v[i];
  bool f = true;
  for(int i=0;i<n;i++) if(v[i]) f = false;
  if(f){
    for(int i=0;i<n;i++) printf("%.8f\n", 0+EPS);
    return 0;
  }
  for(int i=0;i<n;i++){
    for(int j=0;j<=m;j++){
      ps[i][j] = C[m][j] * pow(p[i]/100.0, j) * pow((100 - p[i])/100.0, m - j);
      if(j == 0) s_ps[i][j] = ps[i][j];
      else s_ps[i][j] = s_ps[i][j-1] + ps[i][j];
      ts[i][j] = (double)L / v[i] + t[i] * 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) continue;
        int l = lower_bound(ts[k], ts[k]+m+1, ts[i][j]+EPS) - ts[k];
        if(l != 0) tmp *= (1.0 - s_ps[k][l-1]);
      }
      ans += ps[i][j] * tmp;
    }
    printf("%.8f\n", ans+EPS);
  }
}