An integer N (1 ≤ N ≤ 14), representing some quantity.
An integer M (1 ≤ M ≤ N), representing some quantity.
N pairs of integers (xi, yi) where each integer is between 0 and 10^5.

### Example Input:

```
5 2
0 0
5 5
10 10
100 100
200 200
```

### Function Signature:
Write a function f(N, M, coordinates) that takes in the input.
```python
def f(N: int, M: int, coordinates: List[Tuple[int, int]]):
    '''
    N: an integer
    M: an integer
    coordinates: a list of tuples, each containing two integers
    '''
```