Watch the Marathon

You are a track and field fan and decide to watch a marathon in person. In this race, the course is the line segment connecting the origin on the $XY$ plane and the point $(a, b)$. Because of traffic control during the race, you can watch only from points whose $X$ and $Y$ coordinates are both integers and that are not on the course.

You want to watch from as close to the course as possible. Among the points that satisfy the conditions above, find the point with the smallest Euclidean distance to the course. If several points tie, output the one with the smallest $X$ coordinate. If there is still a tie, output the one with the smallest $Y$ coordinate.

The input consists of at most $300{,}000$ datasets. Each dataset is given in this format:

$a$ $b$

$a$ and $b$ are integers from $1$ to $10^9$, inclusive, and give the coordinates of one endpoint of the marathon course.

The input ends with a line containing two zeros.

For each dataset, print the $X$ and $Y$ coordinates of the best point to watch the race, separated by a space, on one line.