B. Digits Sequence (Hard Edition)
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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

Output

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

Examples
Input
7

Output
7

Input
21

Output
5