Restore the Erased Numbers

During an algebra lesson Liene chose two integers $a$ and $b$ with $0 < |a| < 1000$, $0 < |b| < 1000$, and $a \ge b$. In a single row she wrote four numbers in order: first $a$ and $b$, then $a^2 b$, and finally $ab^2$. She made no calculation mistakes.

For example, the following are valid values of $(a,\ b,\ a^2 b,\ ab^2)$:

Peter erased some of the four numbers and wrote $0$ in their place. Because $a$ and $b$ are nonzero, all four numbers $a$, $b$, $a^2 b$, $ab^2$ are nonzero, so a value of $0$ marks an erased cell.

Given one such (possibly damaged) row of four numbers, restore the original $a$, $b$, $a^2 b$, $ab^2$. If several restorations are possible, output the lexicographically smallest one: the smallest $a$; if $a$ ties, the smallest $b$; then the smallest $a^2 b$; then the smallest $ab^2$. (Because the numbers that were not erased are identical in every valid restoration, this is the same as minimizing the leftmost erased number first, then the remaining erased numbers from left to right.)

One line with four space-separated integers: the possibly damaged row $a$ $b$ $a^2 b$ $ab^2$, where every erased number is written as $0$.

Print the restored row as four space-separated integers $a$ $b$ $a^2 b$ $ab^2$ on one line.

• $0 < |a| < 1000$, $0 < |b| < 1000$
• $a \ge b$
• The input always admits at least one valid restoration.