A12576. Digits Sequence (Hard Edition)

Let's write all the positive integer numbers one after another from $1$ without any delimiters (i.e. as a single string). It will be the infinite sequence starting with 123456789101112131415161718192021222324252627282930313233343536...

Your task is to print the $k$ -th digit of this sequence.

The first and only line contains integer $k$ ( $1 \le k \le 10^{12}$ ) — the position to process ( $1$ -based index).

Print the $k$ -th digit of the resulting infinite sequence.