#900 A Fair Cut

Statement

Statement language

A continuous function $f(x)$ is defined on $[0,L]$ . Its graph is a polyline joining the origin $(0,0)$ and the $N$ points $(x_i,y_i)$ in the given order.

Draw a line through the origin, $g(x)=mx$ . Find a slope $m$ such that the total length of the parts of $[0,L]$ satisfying each of the following inequalities is the same:

$f(x)<g(x)$ .
$g(x)<f(x)$ .

The parts where the two functions are equal contribute to neither length.

If such a slope exists, output its real value $m$ . It may be irrational. Otherwise, print -1.

Input

The input is given in the following format:

$N\ L$ $x_1\ y_1$ $x_{2}$

Output

If a valid slope $m$ exists, print one real number on one line. Your answer is accepted if its absolute or relative error does not exceed $10^{-6}$ .

If no valid slope exists, print -1. This token is a special indication that no solution exists.

Constraints

$1 \le N \le 200\,000$ .
$1 \le L \le 1\,000\,000\,000$ .
.

Subtasks

#	Score	Constraints
1	15	$N=1$ .
2	25	$N \le 20$ .
3	60	No additional constraints.

Samples

Sample 1

Input

1 5
5 10

Output

2.000000000000000

Sample 2

Input

4
0
4

Output

-1

Sample 3

Input

4
1
0

Output

0.333333333333333

Sample 4

Input

Output

0.000000000000000

Sample 5

Input

Output

1.417424305044160