Problem Description
You are given a rooted tree containing N vertices numbered from 1 to N and rooted at vertex numbered 1.
Let's call vertex x a 1-ancestor of vertex y, if x is the parent of vertex y.
Let'c call vertex x a p-ancestor of vertex y, if vertex y has a 1-ancestor, and x is a (p-1)-ancestor of b's 1-ancestor.
You can color each vertex in any of the two possible colours {red, green).
You need to find the total number of different ways to completely color the tree such that in each possible coloring every vertex has a different color assigned then its p-th ancestor.
Return the total number of ways modulo 10° + 7.
NOTE:
.
In the given tree the hierarchy starts from vertex numbered 1.
Two ways are consider different if there exist atleast one vertex that is colored with different colors.
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