Given a table composed of N times M cells, each containing some number of gold coins. You start from the upper left hand corner and at each step may go down or to the right. At each step you collect all the coins that are in that location. Find the maximum number of coins you can collect and the path that provides that result. How many possible paths are there? Please find the exact number of paths that exist and explain why. Give an algorithm to solve this problem with O(NM) time and space. (Pseudo code)