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Nth Digit Finder

Hard
math digit-sequence number-theory optimization
Problem Description

Find the Nth digit in the infinite sequence formed by concatenating positive integers: 123456789101112131415... The sequence starts with 1 and continues indefinitely.

Input Format
A single integer N (1-indexed position).
Output Format
The Nth digit in the sequence.
Constraints
• 1 ≤ N ≤ 10^9

• Sequence: 123456789101112131415...

• 1-indexed (first digit is 1)

• Handle large N efficiently

• Don't generate entire sequence
Sample Input/Output
Input: 
15
Output: 
2
Explanation

Sequence: 123456789101112... Position 15 contains digit 2 (from number 12).

Solution Hints
120
Points
3000ms
Time Limit
256MB
Memory Limit
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