Bob has been given a boring math problem:

Find a set of $3$ non-negative integers denoted as $X$, $Y$, and $Z$, which satisfy the following two equations:

• $X \cdot Y \cdot Z = A$
• $X^2 + Y^2 + Z^2 = B$

Bob has too little time to do this problem. Can you do this for Bob instead?

Input Specification

The first line of the input will contain two integers $A$ and $B$, where $0 \le A, B \le 10^6$.

Output Specification

In one line, output the three corresponding integers of $X$, $Y$, and $Z$, each separated by a space. If there is more than one possible solution, choose the one with the smallest $X$ value. If there is still a tie, choose the solution with the smallest $Y$ value.

If there are no possible combinations, output -1 instead.

Sample Input

15 35

Sample Output

1 3 5