Problem Description

There is a grid array with $n$ rows and $m$ columns. The outermost squares are red, and the remaining squares are black.

Given the number of red squares $r$ and the number of black squares $b$, please provide a feasible pair of values for $n$ and $m$.

Input Format

The input consists of a single line with two integers, representing the number of red squares $r$ and the number of black squares $b$ respectively.

Output Format

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

Sample Input and Output

Sample Input #1

8 1

Sample Output #1

3 3

Sample Input #2

10 2

Sample Output #2

4 3

Sample Input #3

24 24

Sample Output #3

8 6

Notes

Sample 2 Explanation

The output grid array is illustrated below, where light squares represent red and dark squares represent black.

Data Range and Constraints

For all test cases, it is guaranteed that $8 \leq r \leq 2 \times 10^6$ and $1 \leq b \leq 2 \times 10^6$. The data ensures that at least one solution exists.

Notes

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

见题面 Input 部分

见题面 Output 部分