Reservoir
Consider a polygonal line with vertices at coordinates (x_1, y_1), (x_2, y_2), (x_3, y_3), …, (x_N, y_N). These coordinates satisfy the conditions x_i < x_i_{+1} and y_i ≠ y_i_{+1} for every i. From the leftmost vertex (x_1, y_1) and the rightmost vertex (x_N, y_N), we draw vertical rays upwards. This flat figure is then transformed into a three-dimensional body with a constant thickness of 1 along the Oz axis.
Based on these rules, a reservoir is constructed: its front and back walls are flat, vertical, and parallel to each other, separated by a distance of 1. The left and right walls, formed by the vertical rays, are also flat, vertical, and parallel. The polygonal line outlines the shape of the bottom. The reservoir is securely fixed, ensuring it remains stable regardless of the bottom's shape or the amount of water it holds.
Water is gradually poured into this reservoir along its left wall, with a total volume of V cubic units. Your task is to calculate the area of the resulting water surface, ignoring any surface phenomena.
Input
The input consists of two integers: the number of vertices N of the polygonal line and the volume of water V, followed by N pairs of integers representing the coordinates in the order x_1 y_1 x_2 y_2 … x_N y_N.
Constraints are as follows: 2 ≤ N ≤ 12,345, 0 ≤ V ≤ 10^12, and the coordinates do not exceed 10^6 in absolute value.
Output
Output the area of the water surface with a precision of 10^−3.