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 <algorithm>
#include <functional>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <string>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <vector>
#include <list>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <bitset>
#include <climits>

#define all(c) (c).begin(), (c).end()
#define rep(i,n) for(int i=0;i<(n);i++)
#define pb(e) push_back(e)
#define mp(a, b) make_pair(a, b)
#define fr first
#define sc second

const int INF=100000000;
int dx[4]={1,0,-1,0};
int dy[4]={0,1,0,-1};
using namespace std;
typedef long long ll;
typedef pair<int,int> Pi;

ll C[51][51];
int N,M,L;
int P[102],T[102],V[102];
double A[102][51];
double B[102][51];

double f(int a,int b) {
    double ret=A[a][b];
    rep(i,N) if(a!=i) {
        double p=0;
        rep(j,M+1) {
            if(B[a][b]<B[i][j]) p+=A[i][j];
        }
        ret*=p;
    }

    return ret;
}
int main() {
    rep(i,51) C[i][0]=1;
    rep(i,51) for(int j=1;j<=i;j++) C[i][j]=C[i-1][j-1]+C[i-1][j];

    cin>>N>>M>>L;
    rep(i,N) cin>>P[i]>>T[i]>>V[i];

    rep(i,N) {
        // j?????????
        rep(j,M+1) {
            double p=C[M][j];
            rep(k,j) p*=P[i]/100.0;
            rep(k,M-j) p*=(100-P[i])/100.0;
            A[i][j]=p;

            double t=0;
            t+=j*T[i];
            t+=1.0*L/V[i];
            B[i][j]=t;
        }
    }

    double ans[102];

    rep(i,N) {
        ans[i]=0;
        rep(j,M+1) {
            ans[i]+=f(i,j);
        }
    }
    rep(i,N) printf("%.20f\n",ans[i]);



    return 0;
}