<p>Given the <code>root</code> of a binary search tree and an integer <code>k</code>, return <code>true</code> <em>if there exist two elements in the BST such that their sum is equal to</em> <code>k</code>, <em>or</em> <code>false</code> <em>otherwise</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/21/sum_tree_1.jpg" style="width: 400px; height: 229px;" />
<pre>
<strong>Input:</strong> root = [5,3,6,2,4,null,7], k = 9
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/21/sum_tree_2.jpg" style="width: 400px; height: 229px;" />
<pre>
<strong>Input:</strong> root = [5,3,6,2,4,null,7], k = 28
<strong>Output:</strong> false
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 10<sup>4</sup>]</code>.</li>
	<li><code>-10<sup>4</sup> &lt;= Node.val &lt;= 10<sup>4</sup></code></li>
	<li><code>root</code> is guaranteed to be a <strong>valid</strong> binary search tree.</li>
	<li><code>-10<sup>5</sup> &lt;= k &lt;= 10<sup>5</sup></code></li>
</ul>

class BSTIterator {
    stack<TreeNode*>st; // using this stack, I'm doing LNR, inorder traversal.
    stack<TreeNode*>revSt; // reverse inorder traversal
    void pushLeftNodes(TreeNode*root){
        while(root){
            st.push(root);
            root = root->left;
        }
    }

    void pushRightNodes(TreeNode*root){
        while(root){
            revSt.push(root);
            root = root->right;
        }
    }
public:
    BSTIterator(TreeNode* root) {
        pushLeftNodes(root);
        pushRightNodes(root);
    }
    
    int next() {
        auto top = st.top();
        st.pop();

        if(top->right)
            pushLeftNodes(top->right);

        return top->val;
    }

    int before() {
        auto top = revSt.top();
        revSt.pop();

        if(top->left)
            pushRightNodes(top->left);

        return top->val;
    }
    
    bool hasNext() {
        return !st.empty();
    }

    bool hasBefore() {
        return !revSt.empty();
    }
};

class Solution {
public:
    bool findTarget(TreeNode* root, int k) {
        if(!root) return false;
        BSTIterator it(root);

        int i = it.next(); // smalled, L -> R
        int j = it.before(); // largest, R -> L

        while(i < j){
            int sum = i + j;
            if(sum == k) return true;
            else if(sum < k)
                i = it.next(); // start++
            else
                j = it.before(); // end--
        }
        return false;
    }
};
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