PerfectPowers | Topcoder Archive

Problem Statement

A number is called a perfect power if it can be written in the form m^k, where m and k are positive integers, and k > 1.
Given two positive integers A and B, find the two perfect powers between A and B, inclusive, that are closest to each other, and return the absolute difference between them. If less than two perfect powers exist in the interval, return -1 instead.

Definition

Class:: PerfectPowers
Method:: nearestCouple
Parameters:: long, long
Returns:: long
Method signature:: long nearestCouple(long A, long B)
(be sure your method is public)

Notes

1 is a perfect power.

Constraints

A will be between 1 and 10^18, inclusive.
B will be between A+1 and 10^18, inclusive.

Examples

```
1
```
```
4
```
```
Returns: 3
```
1 and 4 are the first pair of perfect powers.
```
8
```
```
9
```
```
Returns: 1
```
8 and 9 are the closest pair of perfect powers.
```
10
```
```
15
```
```
Returns: -1
```
No pair of perfect powers is present in the interval.
```
1
```
```
1000000000000000000
```
```
Returns: 1
```
This is the largest possible range, and 8 and 9 are the closest pair of perfect powers.
```
80000
```
```
90000
```
```
Returns: 80
```

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