Code to be written in python:

Correct answer will automatically be awarded the brainliest.

One of the senior wizards Yee Sian was trapped in a maze during a mission. The maze has n * m cells, labelled from (0, 0) to (n-1, m-1). Starting at cell (0, 0), each time Yee Sian can only take one step, either to the right or down. We wish to find out the number of possible paths to the destination (n - 1, m - 1). A sample path is shown in the figure below.

Having learnt the technique of speeding up the pascal function through memoization, you decide to apply it here. If Yee Sian can walk out by himself (number of paths > 0), tell him how many ways there are. Otherwise, report to Grandwizard and send a rescue team.

Write a function num_of_paths that takes in two integers representing the number of rows (n) and columns (m) in a maze and returns an integer value of number of paths from cell (0, 0) to cell (n - 1, m - 1). The table and skeleton code are given to you. Your table is essentially a dictionary that stores (i, j): val pairs which indicate the number of paths from cell (0, 0) to cell (i, j).

Note: You may assume that all inputs n and m are valid. i.e. n > 0, m > 0.

Incomplete Code:
table = {} # table to memoize computed values

def num_of_paths(n, m):
# your code here
pass


Test Cases:

num_of_paths(1, 100) 1
num_of_paths(123, 1) 1
num_of_paths(3, 3) 6
num_of_paths(10, 10) 48620
num_of_paths(28, 56) 3438452994457305131328