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>
using namespace std;

using ld=long double;
int main(){
    int n,m,l;
    cin>>n>>m>>l;
    vector<ld> p(n);
    vector<int> t(n),v(n);
    for(int i=0;i<n;i++){
        cin>>p[i]>>t[i]>>v[i];
        p[i]/=100;
    }

    vector<vector<ld>> pos(n,vector<ld>(m+1,0));
    for(int i=0;i<n;i++){
        for(int j=0;j<=m;j++){
            pos[i][j]=j*log(p[i]+1e-30)+(m-j)*log(1-p[i]+1e-30);
            for(int k=0;k<j;k++){
                pos[i][j]+=log(m-k)-log(k+1);
            }
            pos[i][j]=exp(pos[i][j]);
        }
        // vector<vector<ld>> comb(m+1,vector<ld>(m+1,0));
        // comb[0][0]=1;
        // for(int j=0;j<=m;j++){
        //     for(int k=0;k<=j;k++){
        //         if(k==0){
        //             comb[j][k]=(p[i]==1 ? ld(0) : ld(pow(1-p[i],ld(j))));
        //         }
        //         else if(k==j){
        //             comb[j][k]=(p[i]==0 ? ld(0) : ld(pow(p[i],j)));
        //         }
        //         else{
        //             comb[j][k]=comb[j-1][k-1]*p[i]+comb[j-1][k]*(1-p[i]);
        //         }
        //     }
        // }
        // pos[i]=comb[m];
    }
    vector<vector<ld>> possum(n,vector<ld>(m+2));
    for(int i=0;i<n;i++){
        partial_sum(pos[i].begin(),pos[i].end(),possum[i].begin()+1);
    }

    vector<ld> res(n,0);
    for(int i=0;i<n;i++){
        if(v[i]==0) continue;
        for(int x=0;x<=m;x++){
            ld sc=pos[i][x];
            for(int j=0;j<n;j++){
                if(i==j || v[j]==0) continue;
                ld z=0;
                for(int y=0;y<=m;y++){
                    if(l*v[j]+x*t[i]*v[i]*v[j]<l*v[i]+y*t[j]*v[i]*v[j]){
                        z+=pos[j][y];
                    }
                }
                sc*=z;
            }
            res[i]+=sc;
        }
    }
    cout<<setprecision(8)<<fixed;
    for(int i=0;i<n;i++){
        cout<<res[i]<<endl;
    }

    return 0;
}