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 <math.h>
#include <utility>
#include <string>
#include <vector>
#include <algorithm>
#include <iostream>
using namespace std;

int main(){
	int n;
	int m;
	int l;
	cin >> n >> m >> l;
	vector<int> p;
	vector<int> t;
	vector<int> v;
	int a;
	for ( int i = 0; i < n; i++ ) {
		cin >> a;
		p.push_back(a);
		cin >> a;
		t.push_back(a);
		cin >> a;
		v.push_back(a);
	}
	long long int c[51][51] = {0};
	for ( int i = 0; i <= m; i++ ) {
		for ( int j = 0; j <= i; j++ ) {
			if ( j == 0 || j == i ) {
				c[i][j] = 1;
			}else {
				c[i][j] = c[i-1][j-1] + c[i-1][j];
			}
		}
	}
	double goaltime;
	double pro;
	double s;
	for ( int i = 0; i < n; i++ ) {
		s = 0.00;
		if ( v[i] == 0 ) {
			cout << fixed << s << endl;
			continue;
		}
		for ( int x = 0; x <= m; x++ ) {
			goaltime = double(l) / v[i] + t[i] * x;
			pro = pow( 0.01*p[i] , x ) * pow( 1.00 - 0.01*p[i] , m - x ) * c[m][x];
			for ( int j = 0; j < n; j++ ) {
				if ( i == j ) continue;
				if ( v[j] == 0 ) {
					continue;
				}
				double g;
				g = goaltime - double(l) / v[j];
				int y;
				if ( t[j] == 0 ) {
					if ( g >= 0 ) y = m + 1;
				}else {
					y = (int)g / t[j] + 1;
				}
				if ( g < 0 ) y = 0;
				if ( y > m ) {
					pro = 0.00;
					break;
				}
				double z = 0.00;
				for ( y; y <= m; y++ ) {
					z += pow( 0.01*p[j] , y ) * pow( 1.00 - 0.01*p[j] , m - y ) * c[m][y];
				}
				pro = pro * z;
			}
			s += pro;
		}
		cout << fixed << s << endl;
	}
	return 0;
}