Problem: Problem statement

Real variables $ x_1, x_2, ..., x_N $ satisfy the following conditions.

1. $ 0 \ leq x_i \ leq 1 $ ($ 1 \ leq i \ leq N $)
2. $ w_1x_1 + w_2x_2 + ... + w_Nx_N \ leq W $



At this time, find the maximum value that $ v_1x_1 + v_2x_2 + ... + v_Nx_N $ can take. It is known that such a maximum actually exists.

Constraint

* $ 1 \ leq N \ leq 10 ^ 5 $
* $ 1 \ leq W \ leq 10 ^ 5 $
* $ -10 ^ 4 \ leq w_i \ leq 10 ^ 4 $
* $ -10 ^ 4 \ leq v_i \ leq 10 ^ 4 $



input

Input follows the following format. All given numbers are integers.


$ N $ $ W $
$ w_1 $ $ v_1 $
$ w_2 $ $ v_2 $
$ ... $
$ w_N $ $ v_N $

output

Output the maximum possible value of $ v_1x_1 + v_2x_2 + ... + v_Nx_N $ on one line. The output must not have an error greater than $ 10 ^ {-3} $.

Examples

Input

1 1
3 1


Output

0.333333


Input

2 3
3 3
1 2


Output

4.000000


Input

2 1
-1 -3
3 10


Output

3.666667

Solution (in PYTHON3):

Solution:
import heapq
N, W = [int(n) for n in input().split()]
tmpw = 0
tmpv = 0
minheap = []
for i in range(N):
    w, v = [int(n) for n in input().split()]
    if(w < 0):
        tmpw += w
        tmpv += v
        w *= -1
        v *= -1
    if(v > 0):
        if w == 0:
            tmpv += v
        else:
            heapq.heappush(minheap, (-(v/w), w, v))
while(W-tmpw > 1e-9 and not minheap == []):
    p = heapq.heappop(minheap)
    w = p[1]
    v = p[2]
    x = min(1, (W-tmpw)/w)
    tmpw += x*w
    tmpv += x*v
print(tmpv)