I have $n$ numbers that come one by one, and when the last element comes, I want to output $k$ largest elements and those that are ties with the minimal element from this top-$k$ element.

For example, I have $[10, 5, 7, 5, 7, 9, 10]$ and $k = 3$, then I want to output $[10, 7, 7, 9, 10]$.

If I didn't want these ties, I'd probably use min-heap and keep track of top-$k$ elements in that heap, replacing minimum every time larger element comes from the stream. However, with ties I would have to perform searching inside the heap the element if it's already there and only then perform replacement/addition.

What is the best way to keep track of top-k + ties elements from the coming array of integers?

Note: $n>>k$.

I have $n$ numbers that come one by one, and when the last element comes, I want to output $k$ largest elements and those that are ties with the minimal element from this top-$k$ element.

For example, I have $[10, 7, 7, 9, 10, 10]$ and $k = 4$, then I want to output $[10, 9, 10, 10]$. However, if $[10, 7, 7, 9, 10]$ and $k = 4$ I want to output $[10, 7 , 7, 9, 10]$. Note that in the first example number of unique elements is less than $k$.

If I didn't want these ties, I'd probably use min-heap and keep track of top-$k$ elements in that heap, replacing minimum every time larger element comes from the stream. However, with ties I would have to perform searching inside the heap the element if it's already there and only then perform replacement/addition.

What is the best way to keep track of top-k + ties elements from the coming array of integers?

Note: $n>>k$.