# Problem Description
The task involves transforming a 1D array of integers based on a given "vertical axis" (specified by the line_position). The transformation involves folding the array around the vertical axis and merging values on either side of the axis using a specific rule. The output is a new 1D array with transformed values.

# Visual Facts
1. Each example starts with an input 1D array and a specified line_position (indicated by a dashed vertical line).
2. The 1D array is folded along the line_position. Values to the left of the axis are flipped (mirrored) and merged with the corresponding values to the right.
3. The output 1D array has fewer elements than the input 1D array.
4. The merging process involves adding overlapping values:
   - Values to the left of the axis are flipped (mirrored) and added to the corresponding values on the right.
   - If the mirrored values on the left have no corresponding values on the right, it is assumed that the corresponding values on the right are 0, and the addition is performed accordingly.

# Visual Patterns
1. **Folding Mechanism**:
   - The values to the left of the line_position are reversed and then added to the values on the right of the line_position.
   
2. **Output Length**:
   - The length of the output array is determined by the maximum distance between the line_position and either end of the input array.
   - Specifically, the output length is `max(line_position, len(numbers) - line_position)`.

3. **Addition Rule**:
   - For each position `i` in the output array, the value is calculated as `numbers[line_position + i - 1] + numbers[line_position - i]`.

# Solution
from typing import List

def solution(numbers: List[int], line_position: int) -> List[int]:
    """
    You are given a list of numbers. Your task is to generate a new list based on the given dashed line position.

    Input:
    - numbers: A 1D list of integers representing the initial state of the numbers.
    - line_position: An integer indicating the position of the dashed line in the transformation process.

    Output:
    - Return a 1D list of integers that represents the newly generated numbers after the transformation.
    """
    left_part = numbers[:line_position][::-1]
    right_part = numbers[line_position:]
    
    max_length = max(len(left_part), len(right_part))
    result = []
    
    for i in range(max_length):
        left_value = left_part[i] if i < len(left_part) else 0
        right_value = right_part[i] if i < len(right_part) else 0
        merged_value = left_value + right_value
        result.append(merged_value)
        
    return result


# Test Script
def test():
    test_cases = [
        ([1, 2, 3], 1, [3, 3]),
        ([1, 2, 3], 2, [5, 1]),
        ([1, 2, 3, 2, 1], 3, [5, 3, 1]),
        ([1, 2, 3, 2, 1], 2, [5, 3, 1]), 
        ([1, 2, 3, 2, 1], 1, [3, 3, 2, 1]),
        ([1, 2, 3, 4], 3, [7, 2, 1]),
        ([1, 2, 3, 4], 2, [5, 5]),
        ([5, 6, 7, 8], 1, [11, 7, 8]),
        ([1, 1, 1, 0, 1, 1], 4, [1, 2, 1, 1])
    ]

    for numbers, line_position, expected_output in test_cases:
        try:
            output = solution(numbers, line_position)
        except Exception as e:
            error_message = (
                f"An exception occurred while running the test case:\n"
                f"`numbers`: {numbers}\n"
                f"`line_position`: {line_position}\n\n"
                f"Exception: '{str(e)}'"
            )
            assert False, error_message

        if output != expected_output:
            error_message = (
                f"The following Test Case failed:\n"
                f"`numbers`: {numbers}\n"
                f"`line_position`: {line_position}\n\n"
                f"Actual Output: {output}\n"
                f"Expected Output: {expected_output}"
            )
            assert False, error_message

test()