You are given an integer array nums and a nonnegative integer k.

A sequence of integers sub is considered good if there are at most k indices i where $0 \leq i <$ sub.length $- 1$ such that sub[i] != sub[i + 1].

Return the maximum possible length of a good subsequence of nums.

Note: A subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.

Constraints:

• $1 \leq$ nums.length $\leq 5 imes 10^3$

• $1 \leq$ nums[i] $\leq 10^9$

• $0 \leq$ k $\leq \min(50,$ nums.length$)$

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