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 (String) 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