Sort the Leaves

You are given a binary tree with $N$ vertices numbered $1$ through $N$. The root of the tree is vertex $1$. There are two types of vertices: - non-leaf: has exactly two sons — a left son and a right son - leaf: doesn't have sons, but it has an integer *value* Let's denote the number of leaves by $L$. It is guaranteed that the values of all leaves are pairwise distinct numbers between $1$ and $L$