Energetic Node(Hard Version)

**This is the hard version of the problem. The only difference is that, in this version, **$K_i \leq 10^{18}$**.** There’s a [tree](https://en.wikipedia.org/wiki/Tree_(data_structure)) having $N$ nodes, out of which, some nodes are **energetic**. Initially, energy of all the nodes is $0$. In the $i^{th}$ second, every **energetic** node will make the energy of itself and all its neighbours **inc