Fossil Excavation Event

Time limit0.5sMemory limit1024 MB

Summary

Count grid cells (x,y) in [-n,n]^2 where max(|x|,|y|) differs from max(|x|,|y-k|), for n,k up to 1e9.

Level: Medium7 of 10
Topics: Math, Geometry, Implementation, Brute force
Solved: No attempts yet

Problem

[Figure] The field with $n=1$ , $k=2$

To mark the opening of the Yonsei University freshman programming contest, Gukryeol planned to hold a fossil excavation event at the field near the engineering building. The fossil excavation event is an event where participants find fossils buried in the field near the engineering building. However, an experiment inside the engineering building contaminated part of the field with a substance that is extremely dangerous to the human body.

Because of this, Gukryeol postponed the fossil excavation event and decided to carry the uncontaminated soil from the field to another place before holding the event. Since he planned to hire an outside company for this work, he had to know the cost of moving the soil in advance, and to compute it he needed the number of cells that contain uncontaminated soil.

The field is a grid of $[-n,n] \times [-n,n]$ , where the bottom-left cell is $(-n,-n)$ and the top-right cell is $(n,n)$ . If some $x$ , $y$ satisfy $\max(\left| x \right|, \left| y \right|) \ne \max(\left| x \right|, \left| y-k \right|)$ , then the soil at $(x,y)$ is uncontaminated clean soil; otherwise it is contaminated soil. For example, if the field is given as $n=1$ , $k=2$ as in the [Figure], the number of cells that contain uncontaminated soil is 6 in total.

Given $n$ and $k$ , find the number of cells that contain uncontaminated soil.

Input

The first line gives $n$ and $k$ . ( $1 \le n, k \le 1 \, 000 \, 000 \, 000$ )

Output

Print the number of cells that contain uncontaminated soil.

Examples3

Example 1
Input
```
1 1
```
Expected output
```
5
```
Example 2
Input
```
1 2
```
Expected output
```
6
```
Example 3
Input
```
1 3
```
Expected output
```
9
```