AlternateOddEven | Topcoder Archive

Problem Statement

Consider all the positive integers with the property that their digits alternate between being odd and even. The sequence of these numbers begins as follows:

1, 2, ..., 9, 10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, ..., 96, 98, 101, 103, 105, 107, 109, 121, 123, ..., 187, 189, 210, 212, ...

Given K, which is the K-th number in this sequence?

Definition

Class:: AlternateOddEven
Method:: kth
Parameters:: long
Returns:: long
Method signature:: long kth(long K)
(be sure your method is public)

Notes

The answer for each valid test case is guaranteed to fit into a signed 64-bit integer.

Constraints

K will be between 1 and 10^11, inclusive.

Examples

```
9
```
```
Returns: 9
```
The first nine numbers in our sequence (positions 1 to 9) are the nine one-digit positive integers.
```
15
```
```
Returns: 21
```
The next six numbers (in positions 10 to 15) are 10, 12, 14, 16, 18, 21.
```
62
```
```
Returns: 125
```
```
100
```
```
Returns: 290
```

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