Generate a python program that has the following intention:

The intention of the program is to find the maximum sum of a sublist in a given list of numbers. The program uses a dynamic programming approach to solve this problem.

The function max_sublist_sum takes an input list of numbers and finds the maximum sum of a sublist ending at each index in the list. The function initially sets the biggest_until_now variable to 0, which represents the maximum sum of a sublist until the current index.

The for loop iterates through each element in the list and finds the maximum of two sums:

max_ending_here + x: this is the sum of all the elements from the beginning of the list until the current index, including the current element x.
0: this is the sum of all the elements from the beginning of the list until the current index, excluding the current element x. This is used to handle the case when the current element is negative.
The biggest_until_now variable is updated with the maximum of these two sums.

Finally, the function returns the biggest_until_now variable, which represents the maximum sum of a sublist in the given list.