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;

#define rep(i,x,y) for(int i=(x);i<(y);++i)
#define debug(x) #x << "=" << (x)

#ifdef DEBUG
#define _GLIBCXX_DEBUG
#define dump(x) std::cerr << debug(x) << " (L:" << __LINE__ << ")" << std::endl
#else
#define dump(x)
#endif

typedef long long int ll;
typedef pair<int,int> pii;
//template<typename T> using vec=std::vector<T>;

const int inf=1<<30;
const long long int infll=1LL<<58;
const long double eps=1e-9;
const int dx[]={1,0,-1,0},dy[]={0,1,0,-1};

template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec){
    os << "[";
    for (const auto &v : vec) {
    	os << v << ",";
    }
    os << "]";
    return os;
}

void solve(){
    int n,m,l;
    cin >> n >> m >> l;
    vector<long double> p(n),t(n),v(n);
    rep(i,0,n){
        cin >> p[i] >> t[i] >> v[i];
        if(v[i]==0) v[i]=1e-12;
    }

    ll comb[51][51]={};
    rep(i,0,51){
        comb[i][i]=1;
        comb[i][0]=1;
    }
    rep(i,1,51) rep(j,1,i){
        if(i>0 and i>j) comb[i][j]+=comb[i-1][j];
        if(j>0) comb[i][j]+=comb[i-1][j-1];
    }

    vector<unordered_map<int,long double>> x(n);
    rep(i,0,n) rep(j,0,m+1) x[i][t[i]*j]+=powl((100-p[i])/100,m-j)*comb[m][j]*powl(p[i]/100,j);
    rep(i,0,n){
        long double s1=0;
        for(const auto& p1:x[i]){
            long double tmp=p1.second;
            rep(j,0,n){
                if(j==i) continue;
                long double s2=0;
                for(const auto& p2:x[j]) if(p2.first+l/v[j]>p1.first+l/v[i]) s2+=p2.second;
                tmp*=s2;
            }
            s1+=tmp;
        }
        cout << fixed << setprecision(8) << s1 << endl;
    }
}

int main(){
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
    solve();
    return 0;
}