A board has n*m cells, and each cell has a value (positive or negative). The game is to start from the top-left cell, and move right or down or diagonal in each step, and finally reach the cell at the bottom-right cell. The objective is to find the maximum total values you may earn and to find a route that generates the maximum. Use the dynamic programming to model, program this problem, and compute its time complexity. Test your program using several data sets generated by a random number generator.