<p>Given the <code>root</code> of a binary tree, the value of a target node <code>target</code>, and an integer <code>k</code>, return <em>an array of the values of all nodes that have a distance </em><code>k</code><em> from the target node.</em></p>

<p>You can return the answer in <strong>any order</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/06/28/sketch0.png" style="width: 500px; height: 429px;" />
<pre>
<strong>Input:</strong> root = [3,5,1,6,2,0,8,null,null,7,4], target = 5, k = 2
<strong>Output:</strong> [7,4,1]
Explanation: The nodes that are a distance 2 from the target node (with value 5) have values 7, 4, and 1.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> root = [1], target = 1, k = 3
<strong>Output:</strong> []
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 500]</code>.</li>
	<li><code>0 &lt;= Node.val &lt;= 500</code></li>
	<li>All the values <code>Node.val</code> are <strong>unique</strong>.</li>
	<li><code>target</code> is the value of one of the nodes in the tree.</li>
	<li><code>0 &lt;= k &lt;= 1000</code></li>
</ul>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    void getNodesAtDepth(TreeNode* root, vector<int> &result, int k, int dir){
        if (!root || k < 0) 
            return;
        if (k == 0){
            result.push_back(root->val);
        }
        if (dir & 0b10)
            getNodesAtDepth(root->left, result, k-1, 0b11);
        if (dir & 0b01)
            getNodesAtDepth(root->right, result, k-1, 0b11);
    }
    bool getChain(TreeNode* root, TreeNode* target, vector<int> &chain){
        if (!root) return 0;
        if (root == target){
            return 1;
        }
        bool left = getChain(root->left, target, chain);
        bool right = getChain(root->right, target, chain);
        if (left) 
            chain.push_back(0b10);
        if (right)
            chain.push_back(0b01);
        return left || right;
    }
    vector<int> distanceK(TreeNode* root, TreeNode* target, int k) {
        vector<int> result;
        vector<int> chain;
        getNodesAtDepth(target, result, k, 0b11);
        getChain(root, target, chain);
        TreeNode *current = root;
        for (int i = chain.size()-1; i >= 0; i--){
            getNodesAtDepth(current, result, k-(i+1), 0b11-chain.back());
            if (chain.back() == 0b01){
                current = current->right;
            }
            else{
                current = current->left;
            }
            chain.pop_back();
        }
        return result;
    }
};
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