# Programming contests

## DEIK Regionális Programozó Csapatverseny, egyetemi kategória, 2022. december 4.

December 4, 2022 10:00 AM – December 4, 2022 3:15 PM

# gcd

In the interval `[A,B]` we are searching for a pair of different numbers `(x,y)` whose greatest common divisor is as large as possible. If the maximum is attained for several pairs, choose the one whose sum is the smallest.

## Example

In the figure above we tabulated the greatest common divisors for "pairs between" `10` and `20`. It is clear from the table that, on the one hand int the case of `A=10,B=20` the maximum is `10` and it only attained at `(10,20)`. On the other hand in the case of `A=10,B=14` the maximum is `2` which is attained at several locations: `(10,12),(10,14),(12,14)`. In the latter case we only need `(10,12)`, the one with the smallest sum.

## Input Specification

```A B
```

A line with the space separated numbers ` 1 ≤ A < B ≤ 107 `.

## Output Specification

```x y
```

A line with space separated values of `x < y`. Separate them with a space.

## Sample Input 1

1. `10 20`

## Sample Output 1

1. `10 20`

## Sample Input 2

1. `11 103`

## Sample Output 2

1. `51 102`
1. `1000001 10000000`
1. `5000000 10000000`