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 <algorithm>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <cstdlib>
#include <cstring>
#include <string>
#include <vector>
#include <cstdio>
#include <queue>
#include <stack>
#include <cmath>
#include <time.h>
using namespace std;

#define LL long long 
#define clr(x) memset(x,0,sizeof(x))
#define eps 1e-6
#define PI 3.1415926535897932384626433832795028          
#define MAXN 105

struct number{
   
	LL p,t,v;
    double c[MAXN];
	double ps[MAXN];

}mem[MAXN];

LL c[55][55];

void C()
{
	 for(LL i = 0;i < 55; i++ )
	       c[0][i]=1;
	 for(LL i = 1;i < 55; i++ )
	 {
		 for(LL j = i;j < 55; j++ )

			 c[i][j]=c[i-1][j-1]+c[i][j-1];
		 
	 }
	 
}

int main()
{

	LL n,m,l,p,t,v;
	C();
	while(scanf("%lld%lld%lld", &n, &m, &l)!=EOF)
	{
		 for(LL i = 0 ;i < n; i++ )
		 {
			 scanf("%lld%lld%lld", &mem[i].p, &mem[i].t, &mem[i].v); 
			 
			 mem[i].c[0]=l*1.0/mem[i].v;
			 for(int j = 1 ;j <= m; j++)
			 {
				mem[i].c[j]+=mem[i].t+mem[i].c[j-1];
			 }
            mem[i].ps[0]=c[0][m]*pow(mem[i].p/100.0,0.0)*pow(1.0-mem[i].p/100.0,m*1.0);
			for(int j = 1; j <= m; j++ )
				mem[i].ps[j]=c[j][m]*(double)pow(mem[i].p/100.0,j*1.0)*pow(1.0-mem[i].p/100.0,(m-j)*1.0);
			//for(int j = 0; j <= m; j++ )
				//printf("%lf ",mem[i].ps[j]);
		 }

		  for(LL i = 0; i< n ; i++ )
		  {
			  double tp,pp=0.0;
			  for(LL j = 0; j <= m; j++ )
			  {
				  tp=mem[i].ps[j];

				  for(LL k = 0; k < n; k++ )
				  {
					  double t=0.0;
					  if(k==i)
						  continue;
					  for(LL q = 0; q <= m; q++ )
						  if(mem[k].c[q]>mem[i].c[j]+eps)
							  t+=mem[k].ps[q];
					  tp*=t;
				  }

				   pp+=tp;
			  }
			  
			  printf("%lf\n",pp);
		  }
	 
	}
	return 0;
}