Impressed, the Elves issue you a challenge: determine the 30000000th number spoken. For example, given the same starting numbers as above:

• Given 0,3,6, the 30000000th number spoken is 175594.
• Given 1,3,2, the 30000000th number spoken is 2578.
• Given 2,1,3, the 30000000th number spoken is 3544142.
• Given 1,2,3, the 30000000th number spoken is 261214.
• Given 2,3,1, the 30000000th number spoken is 6895259.
• Given 3,2,1, the 30000000th number spoken is 18.
• Given 3,1,2, the 30000000th number spoken is 362.

Assignment

Given your starting numbers, what will be the 30000000th number spoken? Determine this in the following way:

• Write a function recitation that takes two arguments: i) a list of starting numbers (str) and ii) a turn \(n \in \mathbb{N}_0\). The function must return the \(n\)-th number (int) spoken.

Example

>>> recitation('0,3,6', 2020)
436
>>> recitation('1,3,2', 2020)
1
>>> recitation('2,1,3', 2020)
10
>>> recitation('1,2,3', 2020)
27
>>> recitation('2,3,1', 2020)
78
>>> recitation('3,2,1', 2020)
438
>>> recitation('3,1,2', 2020)
1836

>>> recitation('0,3,6', 30000000)
175594
>>> recitation('1,3,2', 30000000)
2578
>>> recitation('2,1,3', 30000000)
3544142
>>> recitation('1,2,3', 30000000)
261214
>>> recitation('2,3,1', 30000000)
6895259
>>> recitation('3,2,1', 30000000)
18
>>> recitation('3,1,2', 30000000)
362