Pyramid Sequence

Time limit1sMemory limit128 MB

Summary

Count the distinct pairs formed at matching positions of two repeating pyramid sequences of heights N and M.

Level: Medium7 of 10
Topics: Number theory, Math
Solved: No attempts yet

Problem

A pyramid sequence of height $H$ is $1, 2, \dots, H-1, H, H-1, \dots, 2, 1, 2, \dots$ , so its first $2H-2$ elements repeat forever. A pyramid sequence of height 1 is 1 repeated forever.

Given two natural numbers $N$ and $M$ , pair up the elements that sit at the same position in the pyramid sequence of height $N$ and the pyramid sequence of height $M$ . Write a program that counts how many different pairs appear.

For $N = 3$ and $M = 4$ the two sequences start like this.

1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1
1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1

The different pairs are (1,1), (2,2), (3,3), (2,4), (1,3), (3,1), so there are 6 of them.

Input

The first line contains two natural numbers $N$ and $M$ separated by a space. ( $1 \le N, M \le 10^9$ )

Output

Print the number of different pairs.

Hint

For $N = 3$ and $M = 5$ the two sequences start like this.

1, 2, 3, 2, 1, 2, 3, 2, 1
1, 2, 3, 4, 5, 4, 3, 2, 1

The different pairs are (1,1), (2,2), (3,3), (2,4), (1,5), so there are 5 of them.

Examples2

Example 1
Input
```
3 5
```
Expected output
```
5
```
Example 2
Input
```
3 4
```
Expected output
```
6
```