p01704 Flowers
Problem Statement

We have planted $N$ flower seeds, all of which come into different flowers. We want to make all the flowers come out together.

Each plant has a value called vitality, which is initially zero. Watering and spreading fertilizers cause changes on it, and the $i$-th plant will come into flower if its vitality is equal to or greater than $\mathit{th}_i$. Note that $\mathit{th}_i$ may be negative because some flowers require no additional nutrition.

Watering effects on all the plants. Watering the plants with $W$ liters of water changes the vitality of the $i$-th plant by $W \times \mathit{vw}_i$ for all $i$ ($1 \le i \le n$), and costs $W \times \mathit{pw}$ yen, where $W$ need not be an integer. $\mathit{vw}_i$ may be negative because some flowers hate water.

We have $N$ kinds of fertilizers, and the $i$-th fertilizer effects only on the $i$-th plant. Spreading $F_i$ kilograms of the $i$-th fertilizer changes the vitality of the $i$-th plant by $F_i \times \mathit{vf}_i$, and costs $F_i \times \mathit{pf}_i$ yen, where $F_i$ need not be an integer as well. Each fertilizer is specially made for the corresponding plant, therefore $\mathit{vf}_i$ is guaranteed to be positive.

Of course, we also want to minimize the cost. Formally, our purpose is described as "to minimize $W \times \mathit{pw} + \sum_{i=1}^{N}(F_i \times \mathit{pf}_i)$ under $W \times \mathit{vw}_i + F_i \times \mathit{vf}_i \ge \mathit{th}_i$, $W \ge 0$, and $F_i \ge 0$ for all $i$ ($1 \le i \le N$)". Your task is to calculate the minimum cost.

Input

The input consists of multiple datasets. The number of datasets does not exceed $100$, and the data size of the input does not exceed $20\mathrm{MB}$. Each dataset is formatted as follows.

> $N$
> $\mathit{pw}$
> $\mathit{vw}_1$ $\mathit{pf}_1$ $\mathit{vf}_1$ $\mathit{th}_1$
> :
> :
> $\mathit{vw}_N$ $\mathit{pf}_N$ $\mathit{vf}_N$ $\mathit{th}_N$

The first line of a dataset contains a single integer $N$, number of flower seeds. The second line of a dataset contains a single integer $\mathit{pw}$, cost of watering one liter. Each of the following $N$ lines describes a flower. The $i$-th line contains four integers, $\mathit{vw}_i$, $\mathit{pf}_i$, $\mathit{vf}_i$, and $\mathit{th}_i$, separated by a space.

You can assume that $1 \le N \le 10^5$, $1 \le \mathit{pw} \le 100$, $-100 \le \mathit{vw}_i \le 100$, $1 \le \mathit{pf}_i \le 100$, $1 \le \mathit{vf}_i \le 100$, and $-100 \le \mathit{th}_i \le 100$.

The end of the input is indicated by a line containing a zero.

Output

For each dataset, output a line containing the minimum cost to make all the flowers come out. The output must have an absolute or relative error at most $10^{-4}$.

Sample Input


3
10
4 3 4 10
5 4 5 20
6 5 6 30
3
7
-4 3 4 -10
5 4 5 20
6 5 6 30
3
1
-4 3 4 -10
-5 4 5 -20
6 5 6 30
3
10
-4 3 4 -10
-5 4 5 -20
-6 5 6 -30
0

Output for the Sample Input


43.5
36
13.5
0





Example

Input

3
10
4 3 4 10
5 4 5 20
6 5 6 30
3
7
-4 3 4 -10
5 4 5 20
6 5 6 30
3
1
-4 3 4 -10
-5 4 5 -20
6 5 6 30
3
10
-4 3 4 -10
-5 4 5 -20
-6 5 6 -30
0


Output

43.5
36
13.5
0
```python
import sys
def main():
    readline = sys.stdin.readline
    write = sys.stdout.write

    def gcd(m, n):
        while n:
            m, n = n, m % n
        return m

    def init(p, q=1):
        g = gcd(p, q)
        return p//g, q//g
    def add(A, B):
        pa, qa = A
        pb, qb = B
        if pa == 0:
            return B
        if pb == 0:
            return A
        g = gcd(qa, qb)
        ra = pa*qb//g + pb*qa//g; rb = qa*qb//g
        g = gcd(ra, rb)
        return ra // g, rb // g

    INF = 10**18
    def cp(X):
        vw, pf, vf, th = X
        if vw == 0:
            return INF
        return th/vw
    while 1:
        N = int(readline())
        if N == 0:
            break
        pw = int(readline())
        P = [list(map(int, readline().split())) for i in range(N)]
        P.append((1, 0, 1, 0))
        P.sort(key=cp)
        A = [init(0)]*(N+1)
        B = [init(0)]*(N+1)
        a = b = init(0)
        a = init(pw)
        for i, (vw, pf, vf, th) in enumerate(P):
            if vw == 0:
                if th > 0:
                    b = add(b, (th*pf, vf))
                continue
            if vw > 0:
                if th^vw >= 0:
                    a = add(a, (-vw*pf, vf))
                    b = add(b, (th*pf, vf))
                    A[i] = init(vw*pf, vf)
                    B[i] = init(-th*pf, vf)
            else:
                if th^vw >= 0:
                    A[i] = init(-vw*pf, vf)
                    B[i] = init(th*pf, vf)
                else:
                    a = add(a, (-vw*pf, vf))
                    b = add(b, (th*pf, vf))
        ans = INF
        for i, (vw, pf, vf, th) in enumerate(P):
            if vw == 0:
                continue
            if th^vw < 0:
                continue
            a = add(a, A[i]); b = add(b, B[i])
            pa, qa = a; pb, qb = b
            v = (pa*th*qb + pb*vw*qa) / (vw * qa * qb)
            if ans + 0.01 < v:
                break
            ans = min(ans, v)
        write("%.016f\n" % ans)
main()

```