An integer \(N\) (1 ≤ \(N\) ≤ 14), representing some quantity or size.
An integer \(M\) (1 ≤ \(M\) ≤ \(N\)), representing some quantity or size.
A list of \(N\) tuples, each containing two integers \((x_i, y_i)\) where \(0 ≤ x_i, y_i ≤ 10^5\).

### 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
    '''
```