You are given an integer array, arr, and an integer, k. Your task is to remove exactly k elements from the array so that the number of distinct integers remaining in the array is minimized. Determine the minimum possible count of unique integers after the removals.

Constraints:

• $1 \leq$ arr.length $\leq 10^3$

• $1 \leq$ arr[i] $\leq 10^5$

• $0 \leq$ k $\leq$ arr.length

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