[ICPC2024 Xi'an I] Triangle

There are three points $A(a, 0)$, $B(0, b)$, $C(0, 0)$ in the plane rectangular coordinate system. Define the size of triangle $ABC$ as the number of squares that belong to it. For integers $x,y$, one square is defined by four points $(x, y)$, $(x + 1, y)$, $(x, y + 1)$, $(x + 1, y + 1)$. We consider a square to belong to a triangle if half or more of it is inside the triangle. For example, when $a = 8, b = 6$, the size of triangle $ABC$ will be $24$. The image below shows which squares are counted in the triangle. 

The first and only line contains two integers $a\ (1\le a\le 10^6)$ and $b\ (1\le b\le 10^6)$.

Print an integer: the size of triangle $ABC$.

6 8

24

5 5

15

1 999999

500000