Question:: Tree Parents Subset

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 $10^9+7.$

Input Format:

The first line contains an integer N$,$ denoting the number of elements in C$.$

the next line contains an integer M$,$ denoting the number of rows in edges.

The next line contains an integer, Two, denoting the number of columns in edges.