Unique Paths /homework in Rust

A robot is located at the top-left corner of a n x m grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any moment of time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

Now consider obstacles are placed in some of the grid's cells. How many unique paths would there be?

An obstacle and empty space is marked as 1 and 0 respectively in the grid.

Note: n and m will be at most 100.

It is guaranteed that the answer can be represented as a 32-bit integer.

Example 1:

Input:
[
  [0,0,0],
  [0,1,0],
  [0,0,0]
]
Output: 2
Explanation:
There is one obstacle in the middle of the 3x3 grid above.
There are two ways to reach the bottom-right corner:
1. Right -> Right -> Down -> Down
2. Down -> Down -> Right -> Right