FoxIntegerLevelOne | Topcoder Archive

Problem Statement

Fox Jiro and Eel Saburo are good friends. One day Saburo found two interesting positive integers: A and B.

On the next day, Saburo met Jiro and wanted to tell him the two integers. However, he managed to forget their values. All Saburo could remember was their greatest common divisor G and their least common multiple L.

You are given two longs: G and L. Find the original integers A and B, and return the value of A+B. If there are multiple pairs of A and B that correspond to G and L, pick the one that minimizes A+B. If it is impossible to find such A and B (i.e., Saburo made a mistake somewhere), return -1.

Definition

Class:: FoxAndGCDLCM
Method:: get
Parameters:: long, long
Returns:: long
Method signature:: long get(long G, long L)
(be sure your method is public)

Notes

The greatest common divisor of two integers a and b is the largest positive integer that divides both a and b without any remainder.
The least common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b.

Constraints

G will be between 1 and 1,000,000,000,000 (10^12), inclusive.
L will be between 1 and 1,000,000,000,000 (10^12), inclusive.

Examples

```
2
```
```
20
```
```
Returns: 14
```
The possible pairs of A and B are {2, 20} and {4, 10}. We need to pick {4, 10} since 4+10 is the smallest sum of A and B.
```
5
```
```
8
```
```
Returns: -1
```
There are no pairs of A and B such that their greatest common divisor is 5 and their least common multiple is 8.
```
1000
```
```
100
```
```
Returns: -1
```
```
100
```
```
1000
```
```
Returns: 700
```
```
10
```
```
950863963000
```
```
Returns: 6298430
```

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