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 <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <sstream>
#include <cstring>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <numeric>
#include <cctype>
#include <tuple>
#include <array>

// BEGIN CUT HERE
#ifdef _MSC_VER
#include <agents.h>
#endif
// END CUT HERE 

#define FOR(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep(i, n) FOR(i, 0, n)
#define ALL(v) begin(v), end(v)
#define REV(v) rbegin(v), rend(v)
#define MEMSET(v, s) memset(v, s, sizeof(v))
#define MP make_pair
#define MT make_tuple
#define X first
#define Y second

using namespace std;

typedef long long ll;
typedef pair<int, int> P;
typedef unsigned long long ull;

const int N = 110;
long long C[N][N];

long double prob[N][N];
long double _time[N][N];

int main(){
	C[0][0] = 1;
	rep(i, N - 1) rep(j, i + 1){
		C[i + 1][j] += C[i][j];
		C[i + 1][j + 1] += C[i][j];
	}

	int n, m, L;
	cin >> n >> m >> L;

	vector<int> p(n), t(n), v(n);
	rep(i, n) cin >> p[i] >> t[i] >> v[i];

	rep(i, n){
		_time[i][0] = (double)L / v[i];
		FOR(j, 1, m + 1) _time[i][j] = _time[i][j - 1] + t[i];

		FOR(j, 0, m + 1){
			prob[i][j] = C[m][j] * pow(p[i] / 100., j) * pow((1 - p[i] / 100.), m - j);
			//cout << pow(p[i] / 100., j) << ' ' << pow(1 - p[i] / 100., m-j) << endl;
		}
	}

	cout.setf(ios::fixed);
	cout.precision(10);

	rep(i, n){
		long double a = 0;
		if (v[i]) rep(j, m + 1){
			long double ct = _time[i][j];
			long double cp = prob[i][j];
			rep(k, n){
				if (i == k) continue;
				int idx = m;
				long double tmp = 0;
				while (idx >= 0 && _time[k][idx] > ct) tmp += prob[k][idx--];
				cp *= tmp;
			}
			a += cp;
		}
		cout << a << endl;
	}


	return 0;
}