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.*;

public class Main{

	private void doit(){
		Scanner sc = new Scanner(System.in);
		while(sc.hasNext()){
			int n = sc.nextInt();
			int m = sc.nextInt();
			int l = sc.nextInt();
			int [][] data = new int[n][3];
			for(int i = 0; i < n; i++){
				for(int j = 0; j < 3; j++){
					data[i][j] = sc.nextInt();
				}
			}
			double [][][] dp = new double[n][m+1][m+1];
			for(int i = 0; i < n; i++){
				dp[i][0][0] = 1.0;
				for(int j = 0; j < m; j++){
					for(int k = 0; k < m; k++){
						dp[i][j + 1][k] += dp[i][j][k] * (100 - data[i][0]) / 100;
						dp[i][j + 1][k+1] += dp[i][j][k] * (data[i][0]) / 100;
					}
				}
			}

			for(int i = 0; i < n; i++){
				double prob = 0;
				for(int j = 0; j <= m; j++){
					double sec = (double) l / data[i][2] + j * data[i][1];
					double nowsum = dp[i][m][j];
					for(int k = 0; k < n; k++){
						if(i == k) continue;
						double sum2 = 0;
						for(int kk = 0; kk <= m; kk++){
							double opsec = (double) l / data[k][2] + kk * data[k][1];
							if(opsec > sec){
								sum2 += dp[k][m][kk];
							}
						}
						nowsum *= sum2;
					}
					prob += nowsum;
				}
				System.out.printf("%.6f\n",prob);
			}
		}
	}

	private void debug(Object... o) {
		System.out.println("debug = " + Arrays.deepToString(o));
	}

	public static void main(String[] args) {
		new Main().doit();
	}
}