Canonicalized Input Description:

An integer n (1 ≤ n ≤ 5 × 10^4), representing some quantity or size.
An integer m (1 ≤ m ≤ 5 × 10^4), representing some quantity or size.
An integer k (1 ≤ k ≤ min(10^5, n × m)), representing some quantity or size.
A list of k pairs of integers (xi, yi), where 0 ≤ xi ≤ n−1 and 0 ≤ yi ≤ m−1.

### Example Input:

```
20 10 1
0 0
```

### Function Signature:
Write a function f(n, m, k, coordinates) that takes in the input. 
def f(n: int, m: int, k: int, coordinates: List[Tuple[int, int]]):
    ''' 
    n: an integer 
    m: an integer
    k: an integer
    coordinates: a list of k pairs of integers
    '''
