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 JAVA):

Solution:
import java.util.Scanner;

//Marathon Match
public class Main{

	void run(){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int L = sc.nextInt();
		long[][] comb = new long[51][51];
		comb[0][0] = comb[1][0] = comb[1][1] = 1;
		for(int i=2;i<=50;i++){
			comb[i][0] = comb[i][i] = 1;
			for(int j=1;j<i;j++)comb[i][j] = comb[i-1][j-1]+comb[i-1][j];
		}
		double[] p = new double[n];
		int[] t = new int[n];
		double[] v = new double[n];
		for(int i=0;i<n;i++){
			p[i] = sc.nextDouble()/100.0;
			t[i] = sc.nextInt();
			v[i] = sc.nextDouble();
		}
		double[][] time = new double[n][m+1];
		double[][] pp = new double[n][m+1];
		for(int i=0;i<n;i++){
			double r = L/v[i];
			for(int j=0;j<=m;j++){
				time[i][j] = j*t[i] + r;
				pp[i][j] = comb[m][j]*Math.pow(p[i], j)*Math.pow(1-p[i], m-j);
			}
		}
		for(int i=0;i<n;i++){
			double exp = 0;
			for(int j=0;j<=m;j++){
				double e = pp[i][j];
				for(int k=0;k<n;k++){
					if(i==k)continue;
					double ee = 0;
					for(int l=0;l<=m;l++){
						if(time[i][j]+1e-8<time[k][l])ee += pp[k][l];
					}
					e *= ee;
				}
				exp += e;
			}
			System.out.printf("%.6f\n", exp);
		}
	}
	
	public static void main(String[] args) {
		new Main().run();
	}
}