Coco loves chess. Thinking that the movement of a standard knight is too simple, Coco created a new chess piece called the "K-Knight." A standard knight can move $1$ square horizontally and $2$ squares vertically, or $2$ squares horizontally and $1$ square vertically. The K-Knight is an extension of the knight; in one move, it can move $X$ squares horizontally and $Y$ squares vertically, or $Y$ squares horizontally and $X$ squares vertically.

The Knight Game is a single-player game played on an infinite chocolate grid. In each turn, the player moves the K-Knight according to the rules and eats the chocolate on the square where the K-Knight was previously located. The K-Knight cannot move to a square that does not have chocolate, and the game ends when the K-Knight can no longer make a move.

Coco made Hanbyeol, who lost a game of rock-paper-scissors, play the Knight Game with 99% chocolate and a K-Knight. To help Hanbyeol, who struggles to eat 99% chocolate, determine how to end the game as quickly as possible. The K-Knight starts at $(0, 0)$.

Input

The values $X$ and $Y$, representing the movement rules of the K-Knight, are given in order on a single line.

Output

On the first line, output the number of moves $K$. On the next $K$ lines, output the coordinates to which the K-Knight is moved, one per line in order. Do not output the starting position $(0, 0)$.

Examples

Input 1

1 1

Output 1

7
1 1
2 0
3 -1
2 -2
1 -3
0 -2
1 -1

Note

$0 \le X, Y \le 10^6$, and inputs where both $X$ and $Y$ are $0$ will not be given.