Build a Boat

A modern ship survives a collision because of its bulkheads, reinforced vertical walls inside the hull that keep water that has come in from spreading to other sections.

A design team finished the outline of the cross section of a new ship and left the bulkheads out. Placing them is your job.

The cross section is a simple polygon. A bulkhead is a vertical segment that cuts the whole cross section at one x-coordinate, so a set of bulkheads splits the cross section into vertical sections. Every section must have the same area, and that area must be at least $C$.

Find the largest number of sections $M$ that can be made this way, then report where the bulkheads go.

The first line has an integer $C$ ($10 \le C \le 10^9$), the minimum area of one section.

The second line has an integer $N$ ($3 \le N \le 10^5$), the number of vertices of the outline.

Each of the next $N$ lines has two integers $x$ and $y$ ($-10^4 \le x, y \le 10^4$), the coordinates of one vertex of the hull. The vertices come in counter-clockwise order.

The outline never doubles back on itself horizontally. A vertical line drawn anywhere passes through the cross section exactly once, never twice.

One section of area $C$ always fits, and the number of sections $M$ is between 1 and 100.

On the first line print $M$, the largest number of sections of equal area whose common area is at least $C$.

Then print $M - 1$ lines. Line $k$ holds the x-coordinate of the $k$-th bulkhead, placed so that all $M$ sections have the same area. Print the coordinates in increasing order, each with exactly six digits after the decimal point.