Tree of Trees

You are given $N$ edge-weighted trees $T_1, T_2,\ldots, T_N$ having $M_1, M_2,\ldots ,M_N$ nodes respectively. You also have an array $A$ of $N-1$ positive integers. You need to connect these $N$ trees using $N-1$ edges such that each of these edges have weights equal to $A_i$ for some $i \in [1,N-1]$ and each of the $A_i$ must be used exactly once. Note that after connecting these edges, a singl