report the smallest k-th elements in a min-heap in O(klogk)

Question

I saw online that this is the correct code:

Initialise the min-heap with correct values. Create a priority queue and insert the root node of the min-heap. Write a loop that iterates k - 1 times. Pop the least element from the queue. Add the left and right nodes of the above node into the priority queue. The greatest element in priority queue is the k-th greatest element now. Return it.

But I am not sure about the complexity of removing an element from the priority queue. Also, find the left node and right node of a min-heap should takes O(logn). Thank you.