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:
#define _USE_MATH_DEFINES
#include <algorithm>
#include <cstdio>
#include <functional>
#include <iostream>
#include <cfloat>
#include <climits>
#include <cstring>
#include <cmath>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <time.h>
#include <vector>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> i_i;
typedef pair<ll, int> ll_i;
typedef pair<double, int> d_i;
typedef pair<ll, ll> ll_ll;
typedef pair<double, double> d_d;
struct edge { int u, v; ll w; };

ll MOD = 1000000007;
ll _MOD = 1000000009;
double EPS = 1e-10;

double f(int L, int V, int T, int j) {
	return (double)L / V + j * T;
}

int main() {
	int N, M, L; cin >> N >> M >> L;
	vector<int> P(N), T(N), V(N);
	for (int i = 0; i < N; i++)
		cin >> P[i] >> T[i] >> V[i];
	vector< vector<double> > a(N);
	for (int i = 0; i < N; i++) {
		vector< vector<double> > dp(M + 1, vector<double>(M + 1));
		dp[0][0] = 1;
		for (int j = 0; j < M; j++)
			for (int k = 0; k <= j; k++) {
				dp[j + 1][k] += (1 - P[i] / 100.0) * dp[j][k];
				dp[j + 1][k + 1] += P[i] / 100.0 * dp[j][k];
			}
		a[i] = dp[M];
	}
	for (int i = 0; i < N; i++) {
		double ans = 0;
		for (int j = 0; j <= M; j++) {
			double pro = 1;
			for (int _i = 0; _i < N; _i++) {
				if (_i == i) continue;
				double sum = 0;
				for (int _j = 0; _j <= M; _j++)
					if (f(L, V[i], T[i], j) < f(L, V[_i], T[_i], _j) - EPS)
						sum += a[_i][_j];
				pro *= sum;
			}
			ans += a[i][j] * pro;
		}
		printf("%.10f\n", ans);
	}
}