You are given a tree rooted at node $1$ with N nodes. Each node i has a value C$[$i$-1].$

You need to choose a subset of nodes that satisfies the following conditions:

$1.$ For any two nodes u$,$ v of the chosen subset, if node w is a common ancestor for u and v$,$ then dist$($u$,$w$)!=$ dist$($v$,$w$)$

$2.$ For any two nodes u$,$ v of the chosen subset where dist$($u$,$root$)$ dist$($v$,$root$)-1,$ then parent$[$v$]!=$ u$.$

The value of the subset is the sum of the values of the chosen nodes.

Find the maximum possible value of a chosen subset. Since the answer may be large return it modulo $10^9+7.$