Remove nodes on root to leaf paths of length < K

Given a Binary Tree and a number k, remove all nodes that lie only on root to leaf path(s) of length smaller than k. If a node X lies on multiple root-to-leaf paths and if any of the paths has path length >= k, then X is not deleted from Binary Tree. In other words a node is deleted if all paths going through it have lengths smaller than k.

Consider the following example Binary Tree

               1
           /      \
         2          3
      /     \         \
    4         5        6
  /                   /
 7                   8 
Input: Root of above Binary Tree
       k = 4

Output: The tree should be changed to following  
           1
        /     \
      2          3
     /             \
   4                 6
 /                  /
7                  8
There are 3 paths 
i) 1->2->4->7      path length = 4
ii) 1->2->5        path length = 3
iii) 1->3->6->8    path length = 4 
There is only one path " 1->2->5 " of length smaller than 4.  
The node 5 is the only node that lies only on this path, so 
node 5 is removed.
Nodes 2 and 1 are not removed as they are parts of other paths
of length 4 as well.

If k is 5 or greater than 5, then whole tree is deleted. 

If k is 3 or less than 3, then nothing is deleted.

  
class Solution {
    public Node removeNodesOnSmallerPath(Node node, int level, int k) {
        if (node == null)
            return null;
        if (node.left == null && node.right == null) {
            if (level >= k)
                return node;
            else
                return null;
        }
        node.left = removeNodesOnSmallerPath(node.left, level + 1, k);
        node.right = removeNodesOnSmallerPath(node.right, level + 1, k);

        if (node.left == null && node.right == null)
            return null;
        return node;
    }
}