Hello Group !
I have been trying to solve the "Endless Knight" Problem
( 
http://code.google.com/codejam/contest/dashboard?c=agxjb2RlamFtLXByb2RyEAsSCGNvbnRlc3RzGIL6AQw#s=p3
)

I solved it without much effort but as you can guess
the solution is a dumb Non-polynomial-time solution.
My solution was tree-based solution with the complexity
roughly being 2 to the Power (H or W).

I was wondering if this problem has an actual polynomial time
solution.
In other word, has anyone been able to solve it in polynomial time?

You are welcome to post the whole solution or just a "YES" or "NO"

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