You live in a kingdom which contains N villages and M=(N-1) roads,such that there exists exactly one path between any two villages.You have enough energy to walk exact K hours.You can choose the starting village arbitarily,In one hour,you can go from current village to adjacent village.
How man maximum number of villages can you visit?

The below kingdom represents a tree.It can be rooted at any village.
You are given the parent array having M=(N-1) elements.

function parameters:
parent (integer array): parent[i] denotes parent of node i+1
K(integer): max number of hours you can walk

sample test cases:

Input:M=6(number of roads)
parent=[0,1,1,3,3,3,6]
k=6