BALTIC-WAY 2014 Problem 10

In a country there are 100 airports. Super-Air operates direct flights between some pairs of airports (in both directions). The traffic of an airport is the number of airports it has a direct Super-Air connection with. A new company, Concur-Air, establishes a direct flight between two airports if and only if the sum of their traffics is at least 100. It turns out that there exists a round-trip of Concur-Air flights that lands in every airport exactly once. Show that then there also exists a round-trip of Super-Air flights that lands in every airport exactly once.