Problem:
Marathon Match

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}.

Sample Input 1

2 2 50
30 50 1
30 50 2

Output for the Sample Input 1

0.28770000
0.71230000

Sample Input 2

2 1 100
100 100 10
0 100 1

Output for the Sample Input 2

0.00000000
1.00000000

Sample Input 3

3 1 100
50 1 1
50 1 1
50 1 1

Output for the Sample Input 3

0.12500000
0.12500000
0.12500000

Sample Input 4

2 2 50
30 0 1
30 50 2

Output for the Sample Input 4

0.51000000
0.49000000

Solution in C++14 (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
using LL = long long;

#define fs first
#define sc second

const LL MOD = 1e9+7;
const double EPS = 1e-10;

template<class T>bool chmax(T &a, const T &b) {
    if (a < b) { a = b; return true; }
    return false;
}
template<class T>bool chmin(T &a, const T &b) {
    if (b < a) { a = b; return true; }
    return false;
}

// input
template<typename T>
void input(T& a) { cin >> a; }
template<typename T,typename... Ts>
void input(T& a,Ts&... ts) {
    input<T>(a);
    input<T>(ts...);
}

// std::vector Declaration
template<typename T>
vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts) {
    return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}

// std::vector Initialization
template<typename T>
void fill_all(T& arr, const T& v) { arr = v; }
template<typename T, typename U>
void fill_all(T& arr, const U& v) { for (auto& i : arr) fill_all(i, v); }

// std::vector Input
template<typename T>
istream& operator>>(istream& is, vector<T>& v) {
    for (auto &e : v) {
        is >> e;
    }
    return is;
}

// std::vector Input parallel
template<typename T>
void input_at(size_t idx, T& a) {
    cin >> a[idx];
}
template<typename T, typename... Ts>
void input_at(size_t idx, T& a, Ts&... ts) {
    input_at<T>(idx, a);
    input_at<T>(idx, ts...);
}
template<typename T>
void input_parallel(T& a) {
    for (size_t idx = 0; idx < (size_t)a.size(); ++idx) {
        input_at<T>(idx, a);
    }
}
template<typename T, typename...Ts>
void input_parallel(T& a, Ts&... ts) {
    for (size_t idx = 0; idx < (size_t)a.size(); ++idx) {
        input_at<Ts...>(idx, a, ts...);
    }
}

// std::vector Debug
template<typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "[";
    bool a = 1;
    for (auto e : v) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "]";
    return os;
}

// std::array Debug
template<typename T, size_t n>
ostream& operator<<(ostream& os, const array<T, n>& v) {
    os << "[";
    bool a = 1;
    for (auto e : v) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "]";
    return os;
}

// std::deque Debug
template<typename T>
ostream& operator<<(ostream& os, const deque<T>& d) {
    os << "[";
    bool a = 1;
    for (auto e : d) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "]";
    return os;
}

// std::pair Debug
template<typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << " " << p.second << ")";
    return os;
}

// std::set Debug
template<typename T>
ostream& operator<<(ostream& os, const set<T>& st) {
    os << "{";
    bool a = 1;
    for (auto e : st) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "}";
    return os;
}

// std::multiset Debug
template<typename T>
ostream& operator<<(ostream& os, const multiset<T>& st) {
    os << "{";
    bool a = 1;
    for (auto e : st) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "}";
    return os;
}

// std::map Debug
template<typename T, typename U>
ostream& operator<<(ostream& os, const map<T, U>& mp) {
    os << "{";
    bool a = 1;
    for (auto e : mp) {
        os << (a ? "" : " ");
        os << e.first << ":" << e.second;
        a = 0;
    }
    os << "}";
    return os;
}

// std::tuple Debug
template<int N, class Tuple>
void out(ostream& os, const Tuple& t){}
template<int N, class Tuple, class H, class ...Ts>
void out(ostream& os, const Tuple& t) {
    if (N) os << " ";
    os << get<N>(t);
    out<N+1,Tuple,Ts...>(os, t);
}
template<class ...Ts>
ostream& operator<<(ostream& os, const tuple<Ts...>& t) {
    os << "(";
    out<0,tuple<Ts...>,Ts...>(os, t);
    os << ")";
    return os;
}

// Debug
#define DUMP(x) cerr<<#x<<" = "<<(x)<<endl

// Weighted edge
template<typename T>
struct edge {
    int src, to;
    T cost;

    edge(int to, T cost) : src(-1), to(to), cost(cost) {}
    edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

    edge &operator=(const int &x) {
        to = x;
        return *this;
    }

    operator int() const { return to; }

    friend ostream& operator<<(ostream& os, const edge& e) {
        return os << "(" << e.src << "->" << e.to << ":" << e.cost << ")";
    }
};

template<typename T>
using Edges = vector<edge<T>>;
template<typename T>
using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;
template<typename T>
using MatrixGraph = vector<vector<T>>;

template<typename Field>
struct Comb {
    vector<vector<Field>> c;
    Comb(int n) {
        c.resize(n+1, vector<Field>(n+1));
        for (int i = 0; i <= n; ++i) {
            for (int j = 0; j <= i; ++j) {
                if (j == i || j == 0) {
                    c[i][j] = Field{1};
                } else {
                    c[i][j] = c[i-1][j-1] + c[i-1][j];
                }
            }
        }
    }
    Field operator()(int n, int r) {
        return c[n][r];
    }
};

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

    auto comb = Comb<double>(m);
    auto prob = make_v<double>(n, m+1);
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j <= m; ++j) {
            prob[i][j] = pow(p[i], j) * pow(1-p[i], m-j) * comb(m, j);
        }
    }

    auto ans = make_v<double>(n, m+1);
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j <= m; ++j) {
            double time = L / v[i] + t[i] * j;

            ans[i][j] = prob[i][j];
            for (int k = 0; k < n; ++k) if (i != k) {
                double _p = 0;
                for (int l = 0; l <= m; ++l) {
                    double _t = L / v[k] + t[k] * l;
                    if (_t > time + EPS) break;
                    _p += prob[k][l];
                }
                ans[i][j] *= (1 - _p);
            }
        }
    }

    for (int i = 0; i < n; ++i) {
        double s = accumulate(ans[i].begin(), ans[i].end(), 0.);
        printf("%.7lf\n", s);
    }

    return 0;
}