find the most valuable vertex among all reachable vertices (really hard question)

I have a Directed Graph G=(V,E) that each vertex v has two properties:

• r indicating the worthiness
• m indicating the highest v''s r (where v' is a reachable vertex from v).

I need to find ms for all vertices in O(|V|+|E|) time.

For example,

Initial G

A(r = 1, m = 1) → B(r = 3, m = 3) ← C(r = 2, m = 2)
↓
D(r = 4, m = 4)

has to be

A(r = 1, m = 4) → B(r = 3, m = 3) ← C(r = 2, m = 3)
↓
D(r = 4, m = 4)

I searched SO and found some at Here, but one of the answer does not bound in time and another answer is very badly explained. Is there any simpler idea here?

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