'River crossing puzzle' is the famous classic puzzle. (also known as Wolf, goat and cabbage problem)

summary: The farmer needs to carry wolf, goat and cabbage by boat across the river. Only one can be loaded on the boat at a time. Don't leave wolf and goat on the bank (wolf eats goat). Don't leave goat and cabbage on the bank (goat eats cabbage).

This time, I will extend this puzzle a little. The number of wolves, goat, cabbages and payload is arbitrary.
(see precondition)

You are given four integers as the number of wolves, goats, cabbages and payload of the boat. You have to return the minimum number of boat crossings required to carry all the loads. (If not possible, return None.)

NOTE:

• All loads can live together on the boat.

Example:

river_crossing(1, 1, 1, 1) == 7  # original
river_crossing(1, 1, 1, 2) == 3  # payload +1
river_crossing(2, 1, 1, 2) == 5  # payload +1, wolf +1
river_crossing(1, 2, 1, 1) is None  # impossible

Input: The number of wolves, goats, cabbages and payload (4 integers).

Output: The minimum number of the boat crossings (an integer).

Precondition:

• 1 ≤ wolves + goats + cabbages ≤ 10
• 1 ≤ payload ≤ 5