Let $H$ be a max binary heap with $n$ elements (vertexes).
Pick a vertex $z$ in the heap with height of $k$ ($0<k<\lg n$)
To every element in the sub heap of $z$ we add the constant value $c > 0$.
We need to fix $H$ to be again a max heap, withour changing the value of the elements in the heap.
We need to do it with run time of $O(2^k \cdot \lg n)$.
I know that $MAX-HEAPIFY$ takes $O(\lg n)$ and $2^k$ is the number of leafs in a tree with hright of $k$.
But i dont realy have an idea for an algoritm.