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문제

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

  1. 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.
  2. Edges of the polygon are parallel to either $x$-axis or $y$-axis.
  3. The perimeter of the polygon equals to $l$, while the area equals to $s$.

입력

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

출력

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".

예제 입력 1

4 1

예제 출력 1

4
0 0
1 0
1 1
0 1

예제 입력 2

4 2

예제 출력 2

-1