An integer N (1 ≤ N ≤ 10^5), representing some quantity or size.  
An integer L (1 ≤ L ≤ 10^9), representing some length or distance.  
A list of N tuples, each containing two integers (A_i, B_i), where 1 ≤ A_i ≤ 10^9 and 1 ≤ B_i ≤ 10^9.  
A list of N integers, each containing one integer C_i, where 1 ≤ C_i ≤ 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.
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
    C: a list of integers
    '''