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 <bits/stdc++.h>

using namespace std;

#define int long long
#define all(v) begin(v), end(v)
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define reps(i, s, n) for(int i = (int)(s); i < (int)(n); i++)

const int inf = 1LL << 55;
const int mod = 1e9 + 7;

int N, M, L;
vector<double> P, T, V;

double t[101][51]; // ??°???i???j????????????????????´???????????§?????????

double dp[101][51][51]; // ??°???i????????????j?????§???k??????????¢????

signed main()
{
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);

  cin >> N >> M >> L;
  P.resize(N); T.resize(N); V.resize(N);
  rep(i, N) cin >> P[i] >> T[i] >> V[i], P[i] /= 100;

  rep(i, N) rep(j, M+1) {
    if(V[i]) t[i][j] = L/V[i] + j*T[i];
    else t[i][j] = 1e9;
  }

  rep(i, N) dp[i][0][0] = 1;
  rep(i, N) rep(j, M) rep(k, j+1) {
    dp[i][j+1][k+1] += dp[i][j][k] * P[i];
    dp[i][j+1][k] += dp[i][j][k] * (1 - P[i]);
  }

  rep(i, N) {
    double ans = 0;
    rep(j, M+1) {
      double p = dp[i][M][j];
      rep(k, N) if(i != k) {
	double q = 0;
	rep(l, M+1) if(t[i][j] < t[k][l]) {
	  q += dp[k][M][l];
	}
	p *= q;
      }
      ans += p;
    }
    cout << ans << endl;
  }

  return 0;
}