## Clock sequence

### Problem 506

Consider the infinite repeating sequence of digits:

1234321234321234321...

Amazingly, you can break this sequence of digits into a sequence of integers such that the sum of the digits in the `n`'th value is `n`.

The sequence goes as follows:

1, 2, 3, 4, 32, 123, 43, 2123, 432, 1234, 32123, ...

Let `v _{n}` be the

`n`'th value in this sequence. For example,

`v`

_{2}= 2,

`v`

_{5}= 32 and

`v`

_{11}= 32123.

Let `S`(`n`) be `v`_{1} + `v`_{2} + ... + `v _{n}`. For example,

`S`(11) = 36120, and

`S`(1000) mod 123454321 = 18232686.

Find `S`(10^{14}) mod 123454321.