1177B · Digits Sequence (Hard Edition)

Problem: 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.

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

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