Fractional Knapsack

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

inputFormat

input

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

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

outputFormat

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

样例

1 1
3 1

0.333333