On an infinite field, a robot stands at the coordinates $$$(0; 0)$$$. It needs to reach the point with coordinates $$$(a; b)$$$. In one step, the robot can move one unit up, down, left, or right. Due to the design constraints, the robot can only move in a "zigzag" manner—meaning if the previous step was horizontal, the next one must be vertical, and vice versa. Construct the shortest path for the robot from the starting point to the destination.
Two integers $$$a$$$ and $$$b$$$ are given, each on a separate line ($$$0 \le a, b \le 1000$$$, $$$a + b \gt 0$$$).
Output the coordinates of the robot after each step. Each pair of coordinates should be printed on a separate line, separated by a space. The initial coordinates do not need to be printed. If there are multiple correct answers, you may output any of them.
Solutions that work correctly for $$$a \le 5$$$ and $$$b \le 5$$$ will be scored 40 points.
13
1 0 1 1 0 1 0 2 1 2 1 3
Illustration for the example:
