Guziki

Yogi the bear came up with a new game. He arranged $n^2$ buttons in a square on the table, that is, an $n \times n$ grid with $n$ buttons along each side.

Yogi wonders how many lines pass through the button at the very center of the square such that the number of buttons lying on the line is exactly $g$. Treat every button as a point in the plane.

The first line contains two integers $n$ and $g$ ($1 \le g \le n < 2 \cdot 10^6$, and $n$ is odd).

Print a single integer, the number of lines described above. If that number is greater than $10^{12}$, print $-1$ instead.