Black and White

Arun has a rooted tree of $N$ vertices rooted at vertex $1$. Each vertex can either be coloured black or white. Initially, the vertices are coloured $A_1, A_2, \ldots A_N$, where $A_i \in \{0, 1\}$ denotes the colour of the $i$-th vertex (here $0$ represents white and $1$ represents black). He wants to perform some operations to change the colouring of the vertices to $B_1, B_2, \ldots B_N$ respe