Is the order number in the tree?

Problem

A tree of order numbers is a binary search tree. Given an order number, print YES if the tree holds it and NO if it does not.

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 order number to look for.
Output: YES or NO.
Constraints: 0 ≤ number of nodes ≤ 300
1 ≤ each key ≤ 1000000, all different

Example 1

Input

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

Output

YES

7 is on the path 8, 3, 6, 7.

Example 2

Input

8 3 10 1 6 # 14 # # 4 7 13
5

Output

NO

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

Hint 1

Compare the key with the root and go to one side only.

Hint 2

Stop when you reach a missing child.

Write your Python code, run it on the examples and submit it to hidden tests.