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<vector>
#include<string>
#include<algorithm>	
#include<map>
#include<set>
#include<utility>
#include<cmath>
#include<cstring>
#include<queue>
#include<stack>
#include<cstdio>
#include<sstream>
#include<iomanip>
#include<assert.h>
#define loop(i,a,b) for(int i=a;i<b;i++) 
#define rep(i,a) loop(i,0,a)
#define pb push_back
#define all(in) in.begin(),in.end()
#define shosu(x) fixed<<setprecision(x)
using namespace std;
//kaewasuretyuui
typedef long long ll;
typedef int Def;
typedef pair<Def,Def> pii;
typedef vector<Def> vi;
typedef vector<vi> vvi;
typedef vector<pii> vp;
typedef vector<vp> vvp;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef pair<Def,pii> pip;
typedef vector<pip>vip;
#define mt make_tuple
typedef tuple<double,int,double> tp;
typedef vector<tp> vt;
const double PI=acos(-1);
const double EPS=1e-7;
const int inf=1e9;
const ll INF=2e18;
int dx[]={0,1,0,-1};
int dy[]={1,0,-1,0};
int main(){
	int n,m;
	double l;
	cin>>n>>m>>l;
	vt in;
	rep(i,n){
		double a,b,c;
		cin>>a>>b>>c;
		a/=100;
		double sum=0;
		vd dp(200);
		dp[100]=1;
		rep(j,m){
			vd ndp(200);
			rep(k,200)if(dp[k]>0){
				ndp[k+1]+=dp[k]*a;
				ndp[k-1]+=dp[k]*(1-a);
			}
			dp=ndp;
		}
		rep(j,m+1){
			sum=dp[100-m+2*j];
			if(c)in.pb(tp(l/c+j*b,i,sum));
			else in.pb(tp(inf,i,sum));
		}
	}
	sort(all(in));
	vd out(n);
//	double t=1;
	vd t(n,1);
	rep(i,in.size()){
		double a,c;int b;
		tie(a,b,c)=in[i];
//		cout<<shosu(4)<<a<<" "<<b<<" "<<c<<endl;
		vt tmp;
		tmp.pb(in[i]);
		t[b]-=c;
		while(i!=in.size()-1){
			double d,f;int e;
			tie(d,e,f)=in[i+1];
			if(abs(a-d)<EPS){
				i++;
				tmp.pb(in[i]);
				t[e]-=f;
			}else break;
		}
//		rep(j,t.size())cout<<" "<<t[j];cout<<endl;
		rep(j,tmp.size()){
			double d,f;int e;
			tie(d,e,f)=tmp[j];
			double sum=f;
			rep(k,n)if(k!=e)sum*=t[k];
			out[e]+=sum;
		}
//		cout<<t<<endl;
	}
	rep(i,n)cout<<shosu(9)<<out[i]<<endl;
}