DivisorsPower | Topcoder Archive

Problem Statement

Halina is a young mathematician. Recently she has been studying an interesting function h that operates on positive integers.

Let d(n) be the number of distinct positive divisors of n. The function h is then defined as follows: for each n we have h(n) = n^d(n). In words, h(n) is defined as n to the power of d(n).

For example, d(6)=4 because 6 is divisible by 1, 2, 3, and 6. Then, h(6) = 6^4 = 1296.

Halina already knows how to compute her function h. Now she would like to compute the inverse function. Help her!

You are given a long n. Return the smallest x such that h(x) = n. If there is no such x, return -1 instead.

Definition

Class:: DivisorsPower
Method:: findArgument
Parameters:: long
Returns:: long
Method signature:: long findArgument(long n)
(be sure your method is public)

Constraints

n will be between 2 and 10^18, inclusive.

Examples

```
4
```
```
Returns: 2
```
d(2) = 2, h(2) = 4
```
10
```
```
Returns: -1
```
There is no x satisfying h(x) = 10.
```
64
```
```
Returns: 4
```
d(4) = 3, h(4) = 64
```
10000
```
```
Returns: 10
```
d(10) = 4, h(10) = 10000
```
2498388559757689
```
```
Returns: 49983883
```

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