 Frankfurt UAS, KMITL, VGU & SPbGUT - Combinatorics & Number Theory

#### Start

2017-03-26 21:00 AKDT

## Frankfurt UAS, KMITL, VGU & SPbGUT - Combinatorics & Number Theory

#### End

2017-03-30 10:00 AKDT
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# Problem JThree Powers

Consider the set of all non-negative integer powers of 3.

• $S = \{ 1, 3, 9, 27, 81, \ldots \}$

Consider the sequence of all subsets of $S$ ordered by the value of the sum of their elements. The question is simple: find the set at the $n$-th position in the sequence and print it in increasing order of its elements.

## Input

Each line of input contains a number $n$, which is a positive integer with no more than $19$ digits. The last line of input contains $0$ and it should not be processed. There are at most $100$ test cases.

## Output

For each line of input, output a single line displaying the $n$-th set as described above, in the format used in the sample output.

Sample Input 1 Sample Output 1
1
7
14
783
1125900981634049
0

{ }
{ 3, 9 }
{ 1, 9, 27 }
{ 3, 9, 27, 6561, 19683 }
{ 59049, 3486784401, 205891132094649, 717897987691852588770249 }