An integer N (1 ≤ N ≤ 10^5) and an integer L (1 ≤ L ≤ 10^9), representing some quantities or sizes.
A list of tuples of size N, where each tuple contains two integers (1 ≤ A_i ≤ 10^9) and (1 ≤ B_i ≤ 10^9).
A list of integers C of size N, where each integer is between 1 and 10^9.

### Example Input:

```
3 9
6 3
5 2
3 1
2
2
2
```

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