Pyramid Sequences

A pyramid sequence of height $X$ (with $X > 1$) has period $2X-2$. The first $2X-2$ terms of one period are $1, 2, \ldots, X-1, X, X-1, \ldots, 2$, and the sequence repeats that block forever. Terms are numbered from 1, as $A[1], A[2], \ldots$.

You are given the heights $N$ and $M$ of two pyramid sequences $A$ and $B$. Count how many distinct ordered pairs $(A[i], B[i])$ occur over all $i \ge 1$.

The first line contains $N$ and $M$, separated by a space. ($2 \le N, M \le 10^9$)

Print the number of distinct ordered pairs $(A[i], B[i])$ on the first line.

For $N = 3$ and $M = 4$ the two sequences are:

• $A$: 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, ...
• $B$: 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, ...

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