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 <cstdio>
#include <cstring>
#include <cmath>
using namespace std;

const int MAXN = 105;
const int MAXM = 55;


int N, M, L;
int P[MAXN], T[MAXN], V[MAXN];
long long C[MAXM][MAXM];
void init() {
    C[0][0] = 1;
    for(int i = 1; i < MAXM; i++) {
        C[i][0] = 1;
        for(int j = 1; j <= i; j++)
            C[i][j] = C[i][j - 1] * (i - j + 1) / j;
    }
}

double ans[MAXN];
void calc(int cur_id) {
    if(V[cur_id] == 0) {
        ans[cur_id] = 0;
        return ;
    }
    double res = 0;
    for(int k = 0; k <= M; k++) {
        double ts = 1.0 * L / V[cur_id] + T[cur_id] * k;
        double pk = pow(1.0 * P[cur_id] / 100, k) * pow(1 - 1.0 * P[cur_id] / 100, M - k) * C[M][k];
        double res1 = 1;
        for(int i = 0; i < N; i++) if(i != cur_id) {
            if(V[i] == 0) continue;
            double ti = 1.0 * L / V[i];
            if(T[i] == 0) {
                res1 *= ts < ti ? 1 : 0;
                continue;
            }
            int k = (int)((ts - ti) / T[i] + 1.00000001);
            if(k < 0) continue;
            //k++;
            double pi = 0;
            for(int j = k; j <= M; j++) {
                pi += pow(1.0 * P[i] / 100, j) * pow(1 - 1.0 * P[i] / 100, M - j) * C[M][j];
            }
            res1 *= pi;
        }
        res += res1 * pk;
    }

    ans[cur_id] = res;
}
int main() {
  //  freopen("in.txt", "r", stdin);
    init();
    while(scanf("%d%d%d", &N, &M, &L) != EOF) {
        for(int i = 0; i < N; i++)
            scanf("%d%d%d", &P[i], &T[i], &V[i]);
        for(int i = 0; i < N; i++) {
            calc(i);
        }
        for(int i = 0; i < N; i++)
            printf("%.10f\n", ans[i]);
    }
    return 0;
}