B. Beautiful Handsome's Canteen
time limit per test
2 s
memory limit per test
256 megabytes
input
standard input
output
standard output

Balloon was going to eat lunch at summer school in Handsome's canteen, and his friends Icarus and Sam Well left him alone on this journey. Unfortunately, the path to Handsome's canteen was steep, and he had to go up and down through many hills.

However, Balloon got tired after walking $$$K$$$ meters and fainted from the heat. When he lay down, he remembered how good his life was and how high he had to go. You're given the sequence of points in the path to Handsome's canteen, in which the first point describes the location Balloon starts, and your task is to answer how high in the $$$y$$$ axis he has gone before fainting.

Input

The input consists of two lines:

The first line contains two integers $$$n$$$, $$$K$$$ ($$$2\le n \le 2 \cdot 10^5$$$, $$$0 \le K\le 10^{18}$$$), the number of points and the distance Balloon walked, respectively, in meters.

Then $$$n$$$ lines follow. The $$$i$$$-th line contains two integers describing the point $$$p_i$$$: $$$x_i$$$, $$$y_i$$$ ($$$0 \le x_i, y_i \le 10^9$$$), and it is guaranteed they are ordered by $$$x$$$, and no two points have the same $$$x$$$ coordinate; that means $$$x_i \lt x_{i+1}$$$ for $$$ 1 \le i \lt n$$$.

Output

The output must contain a single line with the real number $$$H$$$, the maximum height he reached. The printed number should have absolute or relative error not exceeding $$$10^{-4}$$$.

Examples
Input
8 22
0 7
4 6
6 1
8 1
10 4
13 5
14 8
16 7
Output
8.000000
Input
8 19
0 7
4 6
6 1
8 1
10 4
13 5
14 8
16 7
Output
7.000000
Note

The path is determined as the sequence of straight segments between every two adjacent points.

The height of a point $$$$$$p_i=(x_i,y_i)$$$$$$ is described by $$$y_i$$$.

Both sample tests are illustrated in the image: the path from $$$A$$$ to $$$G$$$ is approximately $$$21.4 m$$$, so for $$$K = 22 m$$$, he'll go past the point $$$G$$$, achieving the maximum height of $$$8$$$.