Burn a Tree

Given a binary tree denoted by root node A and a leaf node B from this tree.

It is known that all nodes connected to a given node (left child, right child and parent) get burned in 1 second. Then all the nodes which are connected through one intermediate get burned in 2 seconds, and so on.

You need to find the minimum time required to burn the complete binary tree.

2 <= number of nodes <= 10⁵

1 <= node value, B <= 10⁵

node value will be distinct

First argument is a root node of the binary tree, A.

Second argument is an integer B denoting the node value of leaf node.

Return an integer denoting the minimum time required to burn the complete binary tree.

Input 1:

 Tree :      1 
            / \ 
           2   3 
          /   / \
         4   5   6
 B = 4

Input 2:

 Tree :      1
            / \
           2   3
          /     \
         4       5 
 B = 5 

Output 1:

 4

Output 2:

 4

Explanation 1:

 After 1 sec: Node 4 and 2 will be burnt. 
 After 2 sec: Node 4, 2, 1 will be burnt.
 After 3 sec: Node 4, 2, 1, 3 will be burnt.
 After 4 sec: Node 4, 2, 1, 3, 5, 6(whole tree) will be burnt.
 

Explanation 2:

 After 1 sec: Node 5 and 3 will be burnt. 
 After 2 sec: Node 5, 3, 1 will be burnt.
 After 3 sec: Node 5, 3, 1, 2 will be burnt.
 After 4 sec: Node 5, 3, 1, 2, 4(whole tree) will be burnt.