##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
The core idea
Each cell can be reached from the cell above or the cell to the left.
dp[i][j] = number of paths to reach cell (i, j).
Recurrence: dp[i][j] = dp[i-1][j] + dp[i][j-1].
Base: first row and first column have only 1 path each (can only go straight right or straight down).
Answer: dp[m-1][n-1].
