The Fibonacci sequence is a sequence of integer values, beginning with 0 and 1, where each term (after the first two) is equal to the sum of the two preceding terms. For example, the first few terms of the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.

This type of behavior can be used to develop a type of pseudorandom number generator called an Additive Lagged Fibonacci Generator (used in things like the Soviet VIC cipher from the 1950s). The process described below is often called “chain addition”.

Each number or term in the sequence is a single digit. To generate the next term in the sequence, we add two adjacent digits from the sequence, modulo 10, and append the new digit to the end of the sequence. We always begin with the first two digits (elements) of the starting sequence.

Example:
1. Consider the starting list
                  7; 2; 9; 1; 6; 7
The first two digits are 7 and 2. 7 + 2 modulo 10 is 9, so we append 9 to the end of the list to get
                   7; 2; 9; 1; 6; 7; 9
2. Next, we examine the second and third digits. 2 + 9 is 11. 11 modulo 10 is 1, so we append 1 to the end of the list to get
                  7; 2; 9; 1; 6; 7; 9; 1
3. For the third step, we examine the third and fourth digits. 9 + 1 is 10; 10 modulo 10 is 0, so we append 0 to our list to get
                  7; 2; 9; 1; 6; 7; 9; 1; 0
4. Subsequent terms (digits) in the sequence follow the same general pattern.

 

Complete the alfg() function, which takes two arguments: a list containing an initial integer sequence with at least 2 digits, and a positive integer representing the number of rounds of chained addition to perform. The function returns a new list: either the last five digits of the sequence after all of the requested rounds are complete, or the entire list if it has fewer than five terms (digits).

Examples:

Function Call                               Return Value

alfg([5,0,2], 1)                               [5,0,2,5]
alfg([1,2,3,4], 5)                            [3,5,7,7,8]
alfg([2,6,5,3,9,1], 20)                    [1,7,6,7,1]
alfg([6,7,3,4,5], 40)                       [3,9,4,7,5]