module _26

let division d = 
    let digit = 10 / d
    let mutable remainder = 10 % d
    let mutable quotient = [(digit, remainder)]
    let mutable cycleIndex = None
    while remainder <> 0 && cycleIndex = None do
        remainder <- remainder * 10
        let digit =  remainder / d
        remainder <- remainder % d
        let next = (digit, remainder)
        let cycle = quotient |> List.tryFind (fun e -> e = next)
        if cycle <> None then 
            cycleIndex <- Some(
                 quotient.Length 
                 - (quotient |> List.findIndex (fun e -> e = next)) 
                 - 1)
        else quotient <- next :: quotient
    List.rev quotient |> List.map fst, cycleIndex

let cycleLength d =
    match division d with
    | (_,None) -> 0
    | (q,Some(c)) -> q.Length - c

let longestRecurringCycle =
    [2..1000] 
    |> List.mapi ( fun i d -> (i + 2, cycleLength d))
    |> List.maxBy snd