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>
                                        #include<iostream>
                                        #include<cstdio>
                                        #include<vector>
                                        #include<queue>
                                        #include<map>
                                        #include<cstring>
                                        #include<string>
                                        #include <math.h>
                                        #include<algorithm>
                                    //    #include <boost/multiprecision/cpp_int.hpp>
                                        #include<functional>
                               #define int long long
                                        #define inf  1000000007
                                        #define pa pair<int,int>
                                        #define ll long long
                                        #define pal pair<double,double>
                                        #define ppap pair<pa,int>
                                  
                                        #define ssa pair<string,int>
                                        #define  mp make_pair
                                        #define  pb push_back
                                        #define EPS (1e-10)
                                        #define equals(a,b) (fabs((a)-(b))<EPS)
int dx[4]={0,-1,0,1};
int dy[4]={1,0,-1,0};
                                        using namespace std;
                               			class pa3{
                                        	public:
                                        	int x,y,z;
                                        	pa3(int x=0,int y=0,int z=0):x(x),y(y),z(z) {}
                                        	bool operator < (const pa3 &p) const{
                                        		if(x!=p.x) return x<p.x;
                                        		if(y!=p.y) return y<p.y;
                                        		 return z<p.z;
                                        		//return x != p.x ? x<p.x: y<p.y;
                                        	}
                               				bool operator > (const pa3 &p) const{
                                        		if(x!=p.x) return x>p.x;
                                        		if(y!=p.y) return y>p.y;
                                        		 return z>p.z;
                                        		//return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator == (const pa3 &p) const{
                                        		return x==p.x && y==p.y && z==p.z;
                                        	}
                                        		bool operator != (const pa3 &p) const{
                                        			return !( x==p.x && y==p.y && z==p.z);
                                        	}
                                        
                                        };
                                        
                                        class pa4{
                                        	public:
                                        	double x;
                                        	int y,z,w;
                                        	pa4(double x=0,int y=0,int z=0,int w=0):x(x),y(y),z(z),w(w) {}
                                        	bool operator < (const pa4 &p) const{
                                        		if(x!=p.x) return x<p.x;
                                        		if(y!=p.y) return y<p.y;
                                        		if(z!=p.z)return z<p.z;
                                        		return w<p.w;
                                        		//return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator > (const pa4 &p) const{
                                        		if(x!=p.x) return x>p.x;
                                        		if(y!=p.y) return y>p.y;
                                        		if(z!=p.z)return z>p.z;
                                        		return w>p.w;
                                        		//return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator == (const pa4 &p) const{
                                        		return x==p.x && y==p.y && z==p.z &&w==p.w;
                                        	}
                                        		
                                        
                                        };
                                        class pa2{
                                        	public:
                                        	int x,y;
                                        	pa2(int x=0,int y=0):x(x),y(y) {}
                                        	pa2 operator + (pa2 p) {return pa2(x+p.x,y+p.y);}
                                        	pa2 operator - (pa2 p) {return pa2(x-p.x,y-p.y);}
                                        	bool operator < (const pa2 &p) const{
                                        		return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator == (const pa2 &p) const{
                                        		return abs(x-p.x)==0 && abs(y-p.y)==0;
                                        	}
                                        	bool operator != (const pa2 &p) const{
                                        		return !(abs(x-p.x)==0 && abs(y-p.y)==0);
                                        	}
                                        		
                                        
                                        };
                                        
                                               #define ppa pair<int,pas>
                                        class Point{
                                        	public:
                                        	double x,y;
                                        	Point(double x=0,double y=0):x(x),y(y) {}
                                        	Point operator + (Point p) {return Point(x+p.x,y+p.y);}
                                        	Point operator - (Point p) {return Point(x-p.x,y-p.y);}
                                        	Point operator * (double a) {return Point(x*a,y*a);}
                                        	Point operator / (double a) {return Point(x/a,y/a);}
                                        	double absv() {return sqrt(norm());}
                                        	double norm() {return x*x+y*y;}
                                        	bool operator < (const Point &p) const{
                                        		return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator == (const Point &p) const{
                                        		return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
                                        	}
                                        };
                                        typedef Point Vector;
                                 #define pl pair<int,pas>
                                        struct Segment{
                                        Point p1,p2;
                                        };
                                         double dot(Vector a,Vector b){
                                        	return a.x*b.x+a.y*b.y;
                                        }
                                        double cross(Vector a,Vector b){
                                        	return a.x*b.y-a.y*b.x;
                                        }
                                    
            bool parareru(Point a,Point b,Point c,Point d){
            //	if(abs(cross(a-b,d-c))<EPS)cout<<"dd "<<cross(a-b,d-c)<<endl;
            	return abs(cross(a-b,d-c))<EPS;
            }
            double distance_ls_p(Point a, Point b, Point c) {
              if ( dot(b-a, c-a) < EPS ) return (c-a).absv();
              if ( dot(a-b, c-b) < EPS ) return (c-b).absv();
              return abs(cross(b-a, c-a)) / (b-a).absv();
            }
            bool is_intersected_ls(Segment a,Segment b) {
            	if(a.p1==b.p1||a.p2==b.p1||a.p1==b.p2||a.p2==b.p2) return false;
            	if(parareru((a.p2),(a.p1),(a.p1),(b.p2))&&parareru((a.p2),(a.p1),(a.p1),(b.p1))){
            //		cout<<"sss"<<endl;
            		if(dot(a.p1-b.p1,a.p1-b.p2)<EPS) return true;
            		if(dot(a.p2-b.p1,a.p2-b.p2)<EPS) return true;
            		if(dot(a.p1-b.p1,a.p2-b.p1)<EPS) return true;
            		if(dot(a.p1-b.p2,a.p2-b.p2)<EPS) return true;
            		return false;
            	}
              else return ( cross(a.p2-a.p1, b.p1-a.p1) * cross(a.p2-a.p1, b.p2-a.p1) < EPS ) && ( cross(b.p2-b.p1, a.p1-b.p1) * cross(b.p2-b.p1, a.p2-b.p1) < EPS );
            }
             
            double segment_dis(Segment a,Segment b){
            	if(is_intersected_ls(a,b))return 0;
            	double r=distance_ls_p(a.p1, a.p2, b.p1);
            	r=min(r,distance_ls_p(a.p1, a.p2, b.p2));
            	r=min(r,distance_ls_p(b.p1, b.p2, a.p2));
            	r=min(r,distance_ls_p(b.p1, b.p2, a.p1));
            	return r;
            }
            Point intersection_ls(Segment a, Segment b) {
              Point ba = b.p2-b.p1;
              double d1 = abs(cross(ba, a.p1-b.p1));
              double d2 = abs(cross(ba, a.p2-b.p1));
              double t = d1 / (d1 + d2);
             
              return a.p1 + (a.p2-a.p1) * t;
            }
             
                            string itos( int i ) {
                            ostringstream s ;
                            s << i ;
                            return s.str() ;
                            }
                             
                            int gcd(int v,int b){
                            	if(v>b) return gcd(b,v);
                            	if(v==b) return b;
                            	if(b%v==0) return v;
                            	return gcd(v,b%v);
                            }
             
                            double distans(double x1,double y1,double x2,double y2){
                            	double rr=(x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);
                            	return sqrt(rr);
                            	
                            }
                            
   //         int pr[2000010];
     //       int inv[2000010];
            
            int beki(int wa,int rr,int warukazu){
            	if(rr==0) return 1ll;
            	if(rr==1) return wa%warukazu;
            	if(rr%2==1) return (beki(wa,rr-1,warukazu)*wa)%warukazu;
            	int zx=beki(wa,rr/2,warukazu);
            	return (zx*zx)%warukazu;
            }
            /*
			int comb(int nn,int rr){
				int r=pr[nn]*inv[rr];
				r%=inf;
				r*=inv[nn-rr];
				r%=inf;
				return r;
			}
            
            void gya(int ert){
            	pr[0]=1;
            	for(int i=1;i<ert;i++){
            		pr[i]=(pr[i-1]*i)%inf;
            	}
            	for(int i=0;i<ert;i++) inv[i]=beki(pr[i],inf-2,inf);
            	
            }
             */
			//priority_queue<pa3,vector<pa3>,greater<pa3>> pq;            
             //sort(ve.begin(),ve.end(),greater<int>());
                                     //----------------kokomade tenpure------------
            //vector<double> ans(100000000),ans2(100000000);
int n,m;
double l;
double p[100],t[100],v[100];
double comb[160][160];
double kaku[100][160];
double kaku2[100][160];
vector<pal> ve[110];
double bekijou(double r,double k){
	if(r==0) return 0;
	if(k==1) return r;
	if(k==0) return 1;
	return bekijou(r,k-1)*r;
}

   signed main(){
cin>>n>>m>>l;
   	if(n==1){
   	cout<<1<<endl;
   		return 0;
   	}
   	for(int i=0;i<60;i++)comb[i][0]=1.0,comb[i][i]=1.0;
   	
   	for(int k=1;k<60;k++)for(int j=1;j<k;j++) comb[k][j]=comb[k-1][j-1]+comb[k-1][j];
   	
   	for(int i=0;i<n;i++){
   		cin>>p[i]>>t[i]>>v[i];
   		p[i]/=100;
   	}
   	
   	for(int i=0;i<n;i++)for(int j=0;j<=m;j++){
   	//	cout<<i<<" "<<j<<endl;
   		if(j==0)kaku[i][j]=bekijou(1-p[i],m);
   		else if(j==m) kaku[i][j]=bekijou(p[i],m);
   		else{
   			kaku[i][j]=comb[m][j]*bekijou(p[i],j)*bekijou(1.0-p[i],m-j);
   		}
   		kaku2[i][j]=kaku[i][j];
   	//	cout<<i<<" "<<l/v[i]+j*t[i]<<" "<<kaku2[i][j]<<endl;
   		if(j>0) kaku[i][j]+=kaku[i][j-1];
   		ve[i].pb(mp(l/v[i]+j*t[i],kaku[i][j]));
   	}
 	//cout<<"he"<<endl;
   	for(int i=0;i<n;i++){
   		double ans=0;
   		
   		for(int j=0;j<=m;j++){
   			double d=1;
   			
   			for(int l=0;l<n;l++)if(l!=i){
   				pal er=mp(ve[i][j].first,inf);
   				int r=lower_bound(ve[l].begin(),ve[l].end(),er)-ve[l].begin();
   				if(r!=0){
   					d*=1.0-ve[l][r-1].second;
   				}
   			}
   	//		cout<<i<<" "<<j<<" "<<d<<endl;
   			ans+=kaku2[i][j]*d;
   		}
   		printf("%.10lf\n",ans);
   	}
   	
   	
   	return 0;
        }