<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{

    private:

    stack<TreeNode*> st;
    bool isInc = false;

    void build(TreeNode *root){
        if(!root) return;
        while(root){
            if(isInc){
                st.push(root);
                root = root->left;
            }
            else{
                st.push(root);
                root = root->right;
            }
        }
    }

    public:

    BSTIterator(TreeNode *root, bool isInc){
        this->isInc = isInc;
        build(root);
    }

    int current(){
        if(st.empty()) return -1;
        TreeNode *node = st.top();
        return node->val;
    }

    void next(){
        if(st.empty()) return;
        TreeNode *node = st.top();
        st.pop();
        if(isInc){
            build(node->right);
        }
        else{
            build(node->left);
        }
    }

    bool hasNext(){
        return !st.empty();
    }

};


class Solution {

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

        BSTIterator s(root, 1);
        BSTIterator e(root, 0);

        while(s.hasNext() && e.hasNext()){

            if(s.current() == e.current())
              break;
            
            int sum = s.current() + e.current();

            if(sum == k)
               return true;
            
            else if(sum > k)
               e.next();
            
            else
               s.next();

        }

        return false;

    }
};
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