Two orders that add up

Problem

A binary search tree holds item prices. Given a target, print YES if two different nodes have prices that add up to it, and NO otherwise.

Input: Line 1: the tree in level order, keys separated by spaces, with # for a missing child. The children of a missing node are not listed, and trailing # may be left out. A single # is an empty tree. Line 2: the target.
Output: YES or NO.
Constraints: 0 ≤ number of nodes ≤ 300
1 ≤ each key and target ≤ 2000000, keys all different

Example 1

Input

8 3 10 1 6 # 14 # # 4 7 13
17

Output

YES

Example 2

Input

8 3 10 1 6 # 14 # # 4 7 13
100

Output

NO

Try the problem first. Open one hint at a time.

Hint 1

Inorder gives a sorted list.

Hint 2

Then use one pointer at each end of the sorted list.

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