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<bits/stdc++.h>  
template <class T>  
inline bool rd(T &ret) {  
    char c; int sgn;  
    if(c=getchar(),c==EOF) return 0;  
    while(c!='-'&&(c<'0'||c>'9')) c=getchar();  
    sgn=(c=='-')?-1:1;  
    ret=(c=='-')?0:(c-'0');  
    while(c=getchar(),c>='0'&&c<='9') ret=ret*10+(c-'0');  
    ret*=sgn;  
    return 1;  
}  
template <class T>  
inline void pt(T x) {  
    if (x <0) {  
        putchar('-');  
        x = -x;  
    }  
    if(x>9) pt(x/10);  
    putchar(x%10+'0');  
}  
using namespace std;  
typedef long long ll;  
const int MAXN = 55;  
double C[MAXN+1][MAXN+1];  
void Initial()  
{  
    memset(C, 0, sizeof C);  
    for(int i=0; i<=MAXN; ++i)  
    {  
        C[0][i] = 0.0;  
        C[i][0] = 1.0;  
    }  
    for(int i=1; i<=MAXN; ++i)  
    {  
        for(int j=1; j<=MAXN; ++j)  
        C[i][j] = C[i-1][j] + C[i-1][j-1];  
    }  
}  
const int N = 110;  
int n, m;  
int l, t[N], v[N];  
double p[N];  
double Pow(double x, int y){  
    double ans = 1.0;  
    while(y){  
        if(y&1)ans *= x;  
        x = x*x;  
        y >>= 1;  
    }  
    return ans;  
}  
double work(int x){  
    double ans = 0.0;  
    for(int i = 0; i <= m; i++)  
    {  
        double pp = C[m][i] * Pow(p[x], i) * Pow(1.0-p[x], m-i);  
        for(int j = 1; j <= n; j++)  
        {  
            if(j == x)continue;  
            double siz = 0;  
            for(int k = m; k >= 0; k--)  
            {  
                if(l*v[j] + i*t[x]*v[j]*v[x] < l*v[x] + k*t[j]*v[x]*v[j])  
                    siz += C[m][k] * Pow(p[j], k) * Pow(1.0-p[j], m-k);  
                else break;  
            }  
            pp *= siz;  
        }  
        ans += pp;  
    }  
    return ans;  
}  
void input(){  
    for(int i = 1; i <= n; i++)  
        {  
            rd(p[i]);rd(t[i]);rd(v[i]);  
            p[i] /= 100.0;  
        }  
}  
int main(){  
    Initial();  
    while(cin>>n>>m>>l){  
        input();  
        for(int i = 1; i <= n; i++)  
            printf("%.10f\n", work(i));  
    }  
    return 0;  
}