// Learn more about F# at http://fsharp.org open System let mo = 1000000007L let inline (+%) x y = (x + y) % mo let inline (+%=) (x: byref) y = x <- x +% y let inline ( *% ) x y = x * y % mo let rec modpow a n = if n = 0 then 1L elif n = 1 then a elif n % 2 = 0 then modpow (a *% a) (n / 2) else a *% modpow a (n - 1) let inline (/%) x y = x *% (modpow y ((int) mo - 2)) type Mat = int64 [] [] let inline ( *@ ) (a: Mat) (b: Mat) = let n = a.Length let mutable c: Mat = Array.init n (fun _ -> Array.create n 0L) for i = 0 to n - 1 do for j = 0 to n - 1 do for k = 0 to n - 1 do &c.[i].[j] +%= a.[i].[k] *% b.[k].[j] c let rec matpow a n = if n = 1L then a elif n % 2L = 0L then matpow (a *@ a) (n / 2L) else a *@ matpow a (n - 1L) [] let main argv = let n = stdin.ReadLine() |> int64 let inv6 = 1L /% 6L let p = Array.create 6 0L |> Array.mapFold (fun acc _ -> let y = acc *% inv6 +% inv6 y, acc +% y) 0L |> fst |> Array.append [| 1L |] |> Array.take 6 if n < 6L then printfn "%d" p.[(int) n] else let a: Mat = [| [| 0L; 1L; 0L; 0L; 0L; 0L |] [| 0L; 0L; 1L; 0L; 0L; 0L |] [| 0L; 0L; 0L; 1L; 0L; 0L |] [| 0L; 0L; 0L; 0L; 1L; 0L |] [| 0L; 0L; 0L; 0L; 0L; 1L |] [| inv6; inv6; inv6; inv6; inv6; inv6 |] |] let b = matpow a (n - 5L) let q = [| for i in 0 .. 5 -> Array.map2 ( *% ) b.[i] p |> Array.fold (+%) 0L |] printfn "%d" (Array.last q) 0 // return an integer exit code