EnclosedArea | Topcoder Archive

Problem Statement

Below is a simple ASCII art showing one specific rendering of the digits 0 through 9 on a seven-segment digital display. This particular "font" is the one used in this problem.


 0    1    2    3    4    5    6    7    8    9
+-+  + +  +-+  +-+  + +  +-+  +-+  +-+  +-+  +-+
| |    |    |    |  | |  |    |      |  | |  | |
+ +  + +  +-+  +-+  +-+  +-+  +-+  + +  +-+  +-+
| |    |  |      |    |    |  | |    |  | |    |
+-+  + +  +-+  +-+  + +  +-+  +-+  + +  +-+  +-+

Note that if the individual segments that form a digit touch at their endpoints, some of the digits enclose one or two areas completely: the digits 0, 6 and 9 enclose one area each, the digit 8 encloses two.

This generalizes naturally to arbitrary positive integers. For example, a digital representation of the number 1000 contains three enclosed areas, 8968 contains six, and 12345 contains none.

For a given value E we now consider the sequence of all positive integers that have exactly E enclosed areas in their digital representation. We will assign ordinal numbers to the elements of this sequence, starting with number 0 for the smallest such integer.

Given E and N, return the integer that will have the ordinal number N in the above sequence.

Definition

Class:: EnclosedArea
Method:: construct
Parameters:: int, int
Returns:: long
Method signature:: long construct(int E, int N)
(be sure your method is public)

Notes

For the constraints given below it is guaranteed that the return value is smaller than 10^18 (and therefore fits into a signed 64-bit integer).

Constraints

E will be between 0 and 20, inclusive.
N will be between 0 and 10^9, inclusive.

Examples

```
1
```
```
0
```
```
Returns: 6
```
We want the smallest positive integer with one enclosed area. That integer is 6. (Note that 0 is not a positive integer.)
```
7
```
```
1
```
```
Returns: 8088
```
Here we want the second smallest positive integer with 7 enclosed areas. (The smallest is 6888.)
```
7
```
```
8
```
```
Returns: 8898
```
The first eight integers in this sequence (i.e., those with ordinals 0-7) are 6888, 8088, 8688, 8808, 8868, 8880, 8886, and 8889. The next one is the one we seek.
```
0
```
```
123456789
```
```
Returns: 17125735114
```
Integers with no enclosed areas are simply integers written only using digits 1, 2, 3, 4, 5, and 7. There is a fairly obvious relationship between this sequence and integers written in base 6. Note that the return value does not fit into a 32-bit integer. Watch out for overflows!
```
4
```
```
123456
```
```
Returns: 805519
```

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