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 <bits/stdc++.h>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<string> vs;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<int,P> pip;
typedef vector<pip> vip;
const int inf=1<<27;
const ll INF=1ll<<60;
const double pi=acos(-1);
const double eps=1e-11;
const ll mod=1e9+7;
const int dx[4]={-1,0,1,0},dy[4]={0,-1,0,1};



int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	int n,m;
	double w;
	cin>>n>>m>>w;
	vvd a(n),b(n,vd(m+1));
	for(int i=0;i<n;i++){
		double p,t,v;
		cin>>p>>t>>v;
		vd dp(1);
		dp[0]=1;
		p/=100;
		for(int j=0;j<m;j++){
			vd DP(j+2);
			for(int k=0;k<=j;k++){
				DP[k]+=(1-p)*dp[k];
				DP[k+1]+=p*dp[k];
			}
			dp=DP;
		}
		a[i]=dp;
		for(int j=0;j<=m;j++) b[i][j]=w/v+j*t;
	}
	for(int i=0;i<n;i++){
		double res=0;
		for(int j=0;j<=m;j++){
			double tmp=a[i][j];
			for(int k=0;k<n;k++) if(k!=i){
				double sum=0;
				for(int l=0;l<=m;l++) if(b[k][l]>b[i][j]+eps) sum+=a[k][l];
				tmp*=sum;
			}
			res+=tmp;
		}
		cout<<syosu(9)<<res<<endl;
	}
}