Undirected graph n, m.

Find assignment for each vertex of a positive integer such that its value is strictly smaller than the sum of the values of its neighbors, or report that it doesn't exist.

$$$n, m \leq 2 \cdot 10^5$$$ and the output assignment $$$v_i \leq 2 \cdot 10^5$$$.

L.E.: Hints / ideas are highly appreciated. (Reference for the original problem here on CF as well).