let rec longAddWithoutCarry =
 function
 [], x -> x
 | x, [] -> x
 | hd1 :: tl1, hd2 :: tl2 -> hd1 + hd2 :: longAddWithoutCarry (tl1, tl2)

let longAdd (lst1, lst2) =
 let rec helper = function
 [], [], 0 -> []
 | [], [], carry -> [carry]
 | [], hd :: tl, carry -> (hd + carry) mod 10 :: helper ([], tl, (hd + carry) / 10)
 | hd :: tl, [], carry -> (hd + carry) mod 10 :: helper (tl, [], (hd + carry) / 10)
 | hd1 :: tl1, hd2 :: tl2, carry -> (hd1 + hd2 + carry) mod 10 :: helper (tl1, tl2, (hd1 + hd2 + carry) / 10)
 in
 helper (lst1, lst2, 0)

let multAll prod lst = List.map (fun x -> x * prod) lst
let timesTen lst = 0 :: lst

let rec longMult = function
 [], num2 -> []
 | hd :: tl, num2 -> longAdd (multAll hd num2, timesTen (longMult (tl, num2)));;


longMult ([3; 2; 1], [2; 1]);;
longMult ([2; 1], [3; 2; 1]);;
longMult ([9; 7; 6; 5; 4; 3; 2; 1], [8; 1]);;
longMult ([], [9; 9; 9; 9; 9; 9]);;
longMult ([1], [9; 9; 9; 9; 9; 9]);;
longMult ([1; 1; 1; 1; 1; 1; 1; 1; 1], [1; 1; 1; 1; 1; 1; 1; 1; 1]);;

let rec forever a = forever a;;