Rain
At the Meteorological Research Institute, researchers are investigating how water bodies form on various terrains during rainfall. Due to the complexity of real-world scenarios, they have developed a simplified two-dimensional model where the terrain is represented by its height and length. In this model, the terrain is depicted as an N-segment broken line with vertices (x_0, y_0), ..., (x_N, y_N), where x_0 < x_1 < ... < x_N and y_i ≠ y_j for any i < j. The terrain is flanked by towering vertical mountains at points x_0 and x_N. If the terrain were flat, the entire area would be submerged under a water layer of depth H after rainfall. However, due to the broken line nature of the terrain, water flows into depressions, creating water bodies.
Your task is to determine the maximum depth of these water bodies formed after the rain.
Input
The first line contains a natural number N (1 ≤ N ≤ 100) and H, a real number with three decimal places (0 ≤ H ≤ 10^9). The following N+1 lines each contain two integers x_i, y_i (-10000 ≤ x_i, y_i ≤ 10000, 0 ≤ i ≤ N).
Numbers in each line are separated by spaces.
Output
Output a single number representing the maximum depth of the water bodies, accurate to 4 decimal places.