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

#define DO(n) for ( int ____n = n; ____n-->0; )
#define REP(i, n) for (int i=0;i<n;++i)
#define FOR(i, a, b) for (int i=a;i<b;++i)
#define DWN(i, b, a) for (int i=b-1;i>=a;--i)
#define REP_1(i, n) for (int i=1;i<=n;++i)
#define FOR_1(i, a, b) for (int i=a;i<=b;++i)
#define DWN_1(i, b, a) for (int i=b;i>=a;--i)
#define RST(A) memset(A, 0, sizeof(A))
#define FLC(A, x) memset(A, x, sizeof(A))

typedef double DB;

const int N = int(1e2) + 9, M = int(5e1) + 9;
DB p[N][M], sp[N][M], t[N], t0[N];
int n, m, l;

DB f(int i, DB ti){
    DB z = 1; REP(j, n) if (i != j){
        if (t0[j] + m*t[j] <= ti) return 0;
        REP(k, m+1) if (t0[j] + k*t[j] > ti){
            z *= (1 - sp[j][k]);
            break;
        }
    }
    return z;
}

int main(){

    while (~scanf("%d%d%d", &n, &m, &l)){

        RST(p); REP(i, n){
            int _p, v; scanf("%d%lf%d", &_p, &t[i], &v); t0[i] = (DB) l / v; DB pp = (DB) _p / 100;
            //cout <<" " << pp << endl;
            p[i][0] = 1; DO(m){
                DWN_1(j, m, 1) p[i][j] = p[i][j-1] * pp + p[i][j] * (1-pp);
                p[i][0] = p[i][0] * (1-pp);
            }

            REP_1(j, m) sp[i][j] = sp[i][j-1] + p[i][j-1];
        }

        REP(i, n){
            DB z = 0; REP(j, m+1) z += p[i][j] * f(i, t0[i] + t[i]*j);
            printf("%.9f\n", z);
        }
    }
}