Find the partition

A partition of an integer $n$ will be represented by a non increasing sequence of integers.

The partitions of 7 in lexicographic order are:

• 1 - 1 1 1 1 1 1 1
• 2 - 2 1 1 1 1 1
• 3 - 2 2 1 1 1
• 4 - 2 2 2 1
• 5 - 3 1 1 1 1
• 6 - 3 2 1 1
• 7 - 3 2 2
• 8 - 3 3 1
• 9 - 4 1 1 1
• 10 - 4 2 1
• 11 - 4 3
• 12 - 5 1 1
• 13 - 5 2
• 14 - 6 1
• 15 - 7

and in anti-lexicographic order:

• 1 - 7
• 2 - 6 1
• 3 - 5 2
• 4 - 5 1 1
• 5 - 4 3
• 6 - 4 2 1
• 7 - 4 1 1 1
• 8 - 3 3 1
• 9 - 3 2 2
• 10 - 3 2 1 1
• 11 - 3 1 1 1 1
• 12 - 2 2 2 1
• 13 - 2 2 1 1 1
• 14 - 2 1 1 1 1 1
• 15 - 1 1 1 1 1 1 1

The 10th partition is 4,2,1 in the 1st case and 3,2,1,1 in the 2nd.

What are the ${123456789}^{th}$ partition of 123 in lexicographic and anti-lexicographic order?

Answer format: (Comma delimited values) / (Comma delimited values)

Example: 4,2,1/3,2,1,1

[My timing: 11 sec ]