<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>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
void pushRight(TreeNode* root, stack<TreeNode*>& stBefore) {
    while (root) {
        stBefore.push(root);
        root = root->right;
    }
}

void pushLeft(TreeNode* root,stack<TreeNode*>&stAfter){
    while (root) {
        stAfter.push(root);
        root = root->left;  
    }
}

int getPrev(stack<TreeNode*>&stBefore){
    TreeNode* node = stBefore.top();
    stBefore.pop();
    if(node->left){
        pushRight(node->left,stBefore);
    }
    return node->val;
}
int getNext(stack<TreeNode*>&stAfter){
    TreeNode* node = stAfter.top();
    stAfter.pop();
    if(node->right){
        pushLeft(node->right,stAfter);
    }
    return node->val;
}
public:

bool findTarget(TreeNode* root, int k) {
    if (!root) return false;
    stack<TreeNode*> stAfter; 
    stack<TreeNode*> stBefore; 
    pushLeft(root, stAfter);
    pushRight(root, stBefore);
    
    int low = getNext(stAfter);
    int high = getPrev(stBefore);
    
    while (stAfter.size() > 0 && stBefore.size() > 0 && low < high) {
        int sum = low + high;
        if (sum == k) return true;
        else if (sum < k) {
            if (stAfter.size() > 0) low = getNext(stAfter);
            else break;
        } else {
            if (stBefore.size() > 0) high = getPrev(stBefore);
            else break;
        }
    }
    
    return false;
}
};
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