Contains Nearby Duplicate

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

\( nums[i] = nums[j] \quad \text{and} \quad |i - j| \le k \)

If such a pair exists, output True; otherwise, output False.

Note: The array indices are considered in a 0-based manner.

inputFormat

The input is given via standard input in the following format:

1. An integer n denoting the number of elements in the array.
2. A line with n integers separated by spaces, representing the elements of the array nums.
3. An integer k representing the maximum allowed index difference.

outputFormat

Output a single line to the standard output: True if there exists a duplicate number such that the indices difference is at most k, otherwise False.

## sample

4
1 2 3 1
3

True

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