BigFatInteger2 | Topcoder Archive

Problem Statement

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You are given four ints A, B, C and D. Return "divisible" (quotes for clarity) if A^B is divisible by C^D. Return "not divisible" otherwise.

Definition

Class:: BigFatInteger2
Method:: isDivisible
Parameters:: int, int, int, int
Returns:: String
Method signature:: String isDivisible(int A, int B, int C, int D)
(be sure your method is public)

Notes

The return value is case-sensitive.
Positive integer y divides a positive integer x if and only if there is a positive integer z such that y*z=x. In particular, for each positive integer x, both 1 and x divide x.

Constraints

A, B, C and D will each be between 1 and 1,000,000,000 (109), inclusive.

Examples

```
6
```
```
1
```
```
2
```
```
1
```
```
Returns: "divisible"
```
Here, AB = 61 = 6 and CD = 21 = 2. 6 is divisible by 2.
```
2
```
```
1
```
```
6
```
```
1
```
```
Returns: "not divisible"
```
2 is not divisible by 6.
```
1000000000
```
```
1000000000
```
```
1000000000
```
```
200000000
```
```
Returns: "divisible"
```
Now the numbers are huge, but we can see that AB is divisible by CD from the fact that A=C and B>D.
```
8
```
```
100
```
```
4
```
```
200
```
```
Returns: "not divisible"
```
We can rewrite 8100 as (23)100 = 2300. Similarly, 4200 = (22)200 = 2400. Thus, 8100 is not divisible by 4200.
```
999999937
```
```
1000000000
```
```
999999929
```
```
1
```
```
Returns: "not divisible"
```
Here A and C are distinct prime numbers, which means AB cannot have C as its divisor.
```
2
```
```
2
```
```
4
```
```
1
```
```
Returns: "divisible"
```

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