Describe a pseudocode algorithm for the following problem. You are playing a $2-$player game with

N coins. Each turn the current player must pick up either $1$ or $2$ coins. The winner of the game is the

player that picks up the last coin. Your algorithm should return the number of coins to take on the

first turn to guarantee winning if possible.

You must solve this problem using dynamic programming and give the runtime of your algorithm.