You're given a rectangle of integer dimensions n by m. From the bottom-left corner (0, 0), a light ray is fired at a 45° angle toward the top-right. Each time it hits a side, it reflects perfectly (angle of incidence equals angle of reflection). The question: how many side hits (bounces) occur before the ray reaches any rectangle corner?

Input

• Single line with two integers n and m.
• n and m are the rectangle's side lengths.
• The ray starts exactly at the corner (0, 0) heading up-right at 45°.
• Touching a corner counts as reaching a corner, and the process stops immediately; the final contact is not considered a bounce if it's a corner.
• We define a bounce as a hit on a side that is not a corner.

Output

• Single integer: the number of bounces before first reaching any corner.

Example 1 Input

10 15

Example 1 Output

3