405223: GYM101848 G Too Hot, Too Cold

It's strange that the water temperature in the bathroom is changing during my shower.

Actually, the temperature varies with patterns. The time interval in which I take the shower is [0, z]. Assuming the water temperature initially at time 0 is y, it changes gradually and linearly from y to y + y₁ during the time [0, t₁]; then changes linearly from y + y₁ to y + y₂ during the time [t₁, t₂]; so on and so forth; finally, changes linearly from y + y_n - 1 to y + y_n during the time [t_n - 1, t_n]. Thus, it forms a broken line.

As a human being, I can only do my shower with water temperature between 30 and 30 + h, inclusively. As a lazy human being, I only want to change the water temperature before I start to take the shower. You are asked to find out for how much time at most I can enjoy my shower.

The first line contains two space-separated integers n and h (1 ≤ n ≤ 10⁵, 0 ≤ h ≤ 2·10⁵).

The next n lines each contain two space-separated integers, denoting (t₁, y₁), (t₂, y₂), ..., (t_n, y_n), respectively. (1 ≤ t₁ < t₂ < ... < t_n = z ≤ 10⁶,  - 10⁵ ≤ y_i ≤ 10⁵).

Output the maximum time I can take the shower if I choose the initial temperature optimally. Your answer is required to have absolute or relative error less than 10^- 6.

3 2
50 5
75 2
100 5

53.333333333

2 2
500 2
1000 1

1000.000000000

1 1
1 1

1.000000000

The water temperature can be arbitrarily low, even if this breaks some physical laws.

Figure that will explain Example 1: