Nearby Duplicate Elements

You are given an array of integers and an integer k. Your task is to determine whether there exist two distinct indices i and j in the array such that:

$$ a[i] = a[j] \quad \text{and} \quad |i - j| \le k. $$

This problem tests your ability to efficiently search for duplicate elements within a limited index range using appropriate data structures.

inputFormat

The input is provided via standard input and consists of three lines:

• The first line contains an integer n, representing the number of elements in the array.
• The second line contains n integers separated by spaces, representing the array elements.
• The third line contains an integer k, representing the maximum allowed index difference.

outputFormat

Output a single line to standard output: "True" if there exists a pair of distinct indices i and j satisfying a[i] == a[j] and |i - j| \le k. Otherwise, output "False".

6
1 2 3 1 2 3
2

False