Sonya and Gifts

Sonya lives in a magical land which consists of $N$ cities (numbered $1$ through $N$) and $N - 1$ roads connecting them. In other words, the country where Sonya lives is a tree. The country is magical because toys of an infinite number of types are made there. The types of toys are labeled by all integers and in each city, there is a toy store which sells an infinite number of toys of each type