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>

using namespace std;

#define rep(i, n) for (int i = 0; i < int(n); ++i)

long long nck[60][60];

int main() {
  rep (i, 60) nck[i][i] = 1;
  rep (i, 60) nck[i][0] = 1;
  rep (i, 55) rep (j, i) nck[i + 1][j + 1] = nck[i][j] + nck[i][j + 1];
  int n, m;
  double l;
  cin >> n >> m >> l;
  double p[n], t[n], v[n];
  rep (i, n) cin >> p[i] >> t[i] >> v[i];
  rep (i, n) p[i] /= 100;
  double tt[n][m + 1];
  rep (i, n) rep (j, m + 1) tt[i][j] = l / v[i] + t[i] * j;
  double pp[n][m + 1];
  rep (i, n) rep (j, m + 1) {
    pp[i][j] = nck[m][j];
    rep (k, j) pp[i][j] *= p[i];
    rep (k, m - j) pp[i][j] *= 1 - p[i];
  }
  rep (i, n) {
    double res = 0;
    rep (j, m + 1) {
      double r = pp[i][j];
      rep (ii, n) if (i != ii) {
	double rr = 0;
	rep (jj, m + 1) if (tt[i][j] < tt[ii][jj] - 1e-8) rr += pp[ii][jj];
	r *= rr;
      }
      res += r;
    }
    printf("%.12lf\n", res);
  }
}