Description

There is an $n$ by $m$ grid. The cells on the outer border are red, and all other cells are black.

Given the number of red cells $r$ and the number of black cells $b$, find a feasible pair of values $n$ and $m$.

Input Format

The input consists of one line with two integers, representing the number of red cells $r$ and the number of black cells $b$.

Output Format

Output one line with two integers, representing the number of rows $n$ and the number of columns $m$ of the grid. If there are multiple solutions, output the one with the largest $n$.

8 1

3 3

10 2

4 3

24 24

8 6

Hint

Explanation of Sample 2

The output grid is shown in the figure: light-colored cells represent red, and dark-colored cells represent black.

Constraints

For all testdata, it is guaranteed that $8 \leq r \leq 2 \times 10^6$ and $1 \leq b \leq 2 \times 10^{6}$. It is guaranteed that at least one solution exists.

Note

This problem is translated from COCI2010-2011 CONTEST #4 T2 PARKET. Translation by @一扶苏一.

Translated by ChatGPT 5