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<iostream>
#include<cstdio>
#include<cstring>
#define eps 1e-14
using namespace std;
double f_pow(double x,int n){
	double res=1;
	while(n--)res*=x;
	return res;
}

struct Man{
	double p,t,v;
	void get(){
		scanf("%lf%lf%lf",&p,&t,&v);
		p/=100;
	}
};
Man man[200];
int N,M;
double L;
double tim[200][61],tsum[200][61];
double rate[200][61];
double C[61][61];
void get_C(){
	int i,j;
	C[0][0]=1;
	C[1][0]=C[1][1]=1;
	for(i=2;i<61;i++){
		C[i][0]=C[i][i]=1;
		for(j=1;j<i;j++){
			C[i][j]=C[i-1][j]+C[i-1][j-1];
		}
	}
}
void get_data(){
	scanf("%d%d%lf",&N,&M,&L);
	int i;
	for(i=0;i<N;i++)man[i].get();
}
void get_tim(){
	int i,j;
	for(i=0;i<N;i++){
		rate[i][0]=f_pow(1-man[i].p,M);
		if(man[i].v<eps)tim[i][0]=2000000000;
		else tim[i][0]=L/man[i].v;
		for(j=1;j<=M;j++){
			if(M-j>=j)rate[i][j]=C[M][j]*f_pow(man[i].p*(1-man[i].p),j)*f_pow(1-man[i].p,M-j-j);
			else rate[i][j]=C[M][j]*f_pow(man[i].p*(1-man[i].p),M-j)*f_pow(man[i].p,j+j-M);
			tim[i][j]=tim[i][j-1]+man[i].t;
		}
		tsum[i][M]=rate[i][M];
		for(j=M-1;j>=0;j--)tsum[i][j]=tsum[i][j+1]+rate[i][j];
	}
}
double bina(int ren,double t){
	int h=M,l=0,mid;
	while(h>l){
		mid=(h+l)>>1;
		if(tim[ren][mid]<t+eps)l=mid+1;
		else h=mid;
	}
	return tsum[ren][h];
}
double get_win(int winner,double t){
	int i;
	double res=1;
	for(i=0;i<N;i++){
		if(i==winner)continue;
		if(tim[i][M]<t+eps)return 0;
		res*=bina(i,t);
	}
	return res;
}
void run(){
	int i,j;
	double sum;
	for(i=0;i<N;i++){
		if(man[i].v<eps){
			printf("0.0000000000\n");
			continue;
		}
		sum=0;
		for(j=0;j<=M;j++){
			sum+=rate[i][j]*get_win(i,tim[i][j]);
		}
		printf("%.9lf\n",sum);
	}
}
int main(){
	get_C();
	get_data();
	get_tim();

	run();
	return 0;
}