<p>Given an array of integers&nbsp;<code>arr</code>&nbsp;and an integer <code>k</code>.&nbsp;Find the <em>least number of unique integers</em>&nbsp;after removing <strong>exactly</strong> <code>k</code> elements<b>.</b></p>

<ol>
</ol>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input: </strong>arr = [5,5,4], k = 1
<strong>Output: </strong>1
<strong>Explanation</strong>: Remove the single 4, only 5 is left.
</pre>
<strong class="example">Example 2:</strong>

<pre>
<strong>Input: </strong>arr = [4,3,1,1,3,3,2], k = 3
<strong>Output: </strong>2
<strong>Explanation</strong>: Remove 4, 2 and either one of the two 1s or three 3s. 1 and 3 will be left.</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= arr.length&nbsp;&lt;= 10^5</code></li>
	<li><code>1 &lt;= arr[i] &lt;= 10^9</code></li>
	<li><code>0 &lt;= k&nbsp;&lt;= arr.length</code></li>
</ul>
class Solution:

    def findLeastNumOfUniqueInts(self, arr: List[int], k: int) -> int:
        length = len(arr)
        if length == 1:
            return 0 if k > 0 else 1
        if k == length:
            return 0
            
        arr.sort()
        count_map = {}
        count = 1
        for i in range(1, length):
            if arr[i] == arr[i-1]:
                count += 1
            else:
                if count in count_map:
                    count_map[count] += 1
                else:
                    count_map[count] = 1
                count = 1
        if count in count_map:
            count_map[count] += 1
        else:
            count_map[count] = 1
    

        key_set = set(count_map.keys())
        while k > 0:
            min_key = min(key_set)
            elem_count = min_key * count_map[min_key]
            if (k >= elem_count):
                key_set = key_set - {min_key}
                k -= elem_count
                count_map[min_key] = 0
            else:
                count_map[min_key] -= k//min_key
                break
        
        return sum(count_map.values())
31000