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:
// template {{{

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

#define loop(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rep(i, n) loop(i, 0, n)
#define rloop(i, a, b) for (int i = (int)(b) - 1; i >= (int)(a); i--)
#define rrep(i, n) rloop(i, 0, n)
#define pb push_back
#define pf push_front
#define eb emplace_back
#define ef emplace_front
#define mp std::make_pair
#define mt std::make_tuple
#define fi first
#define se second

using ll = long long;
using ull = unsigned long long;

template<typename T, size_t H, size_t W>
using matrix = std::array<std::array<T, W>, H>;

const int MOD = 1e9 + 7;
const int INF = 1e9 + 10;
const ll LLINF = 1e18 + 10;

const int dx[] = {-1, 0, 1, 0, -1, -1, 1, 1};
const int dy[] = {0, -1, 0, 1, -1, 1, -1, 1};

template<typename T>
inline T sq(T x){ return x * x; }

template<typename T, typename U>
inline void chmax(T &x, U y){ x = std::max<T>(x, y); }

template<typename T, typename U>
inline void chmin(T &x, U y){ x = std::min<T>(x, y); }

template<typename T>
inline void sort(T &c){ std::sort(std::begin(c), std::end(c)); }

template<typename T>
inline void reverse(T &c){ std::reverse(std::begin(c), std::end(c)); }

template<typename T>
inline void unique(T &c){ std::sort(c); c.erase(std::unique(std::begin(c), std::end(c))); }

// }}}

int n, m;
double l;
double p[100], t[100], v[100];
double a[100][60], b[100][60];
double dp[60][60];

double calc(int i, int j, double p)
{
	if (i == 0) return j == 0 ? 1.0 : 0.0;
	if (dp[i][j] > -1.0) return dp[i][j];
	double vl = p * calc(i - 1, j - 1, p);
	double vr = (1.0 - p) * calc(i - 1, j, p);
	return dp[i][j] = vl + vr;
}

int main()
{
	cin >> n >> m >> l;
	rep(i, n){
		cin >> p[i] >> t[i] >> v[i];
		p[i] /= 100;
	}

	rep(i, n){
		fill_n(*dp, 60 * 60, -1.0);
		rep(j, m + 1) a[i][j] = calc(m, j, p[i]);
		rep(j, m + 1) b[i][j] = l / v[i] + t[i] * j;
	}

	rep(i, n){
		double s = 0.0;
		rep(j, m + 1){
			double t = 1.0;
			rep(x, n){
				if (i == x) continue;
				double u = 0.0;
				rep(y, m + 1){
					if (b[i][j] < b[x][y] - 1e-8){
						u += a[x][y];
					}
				}
				t *= u;
			}
			s += t * a[i][j];
		}
		printf("%.20f\n", s);
	}
}