Simple Polygon

Time limit1sMemory limit512 MB

Summary

Given a perimeter l and area s, construct a simple rectilinear polygon with exactly that perimeter and area, or report that none exists.

Level: Hard8 of 10
Topics: Geometry, Math, Implementation, Brute force
Solved: No attempts yet

Problem

Although bobo is truly smart, he just wants you to find a simple polygon for him. The polygon you are going to find should satisfy the following conditions.

The polygon is simple. That is to say, any two non-adjacent edges won't intersect or touch and any two adjacent edges have exactly one common point.
Edges of the polygon are parallel to either the $x$ -axis or the $y$ -axis.
The perimeter of the polygon equals $l$ , while the area equals $s$ .

Input

First line of the input contains two integers $l$ and $s$ ( $4 \leq l \leq 10^9, 1 \leq s \leq 10^9$ ).

Output

The first line contains an integer $n$ , which denotes the number of vertices of the polygon you have found ( $4 \leq n \leq 1000$ ).

Each of the following $n$ lines contains $2$ integers $x\_i, y\_i$ , which denote the coordinates of points (in clockwise or counter-clockwise order) ( $0 \leq x\_i, y\_i \leq 10^9$ ).

Any appropriate solution will get accepted.

If no such polygon can be found, simply print "-1".

Examples2

Example 1
Input
```
4 1
```
Expected output
```
4
0 0
1 0
1 1
0 1
```
Example 2
Input
```
4 2
```
Expected output
```
-1
```