Problem:
Score : 200 points

Problem Statement

Find the sum of the integers between 1 and N (inclusive), whose sum of digits written in base 10 is between A and B (inclusive).

Constraints

1 \leq N \leq 10^4

1 \leq A \leq B \leq 36

All input values are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

Print the sum of the integers between 1 and N (inclusive), whose sum of digits written in base 10 is between A and B (inclusive).

Sample Input 1

20 2 5

Sample Output 1

84

Among the integers not greater than 20, the ones whose sums of digits are between 2 and 5, are: 2,3,4,5,11,12,13,14 and 20. We should print the sum of these, 84.

Sample Input 2

10 1 2

Sample Output 2

13

Sample Input 3

100 4 16

Sample Output 3

4554

Solution in OCaml (4.02.3) (judge verdict: Accepted)

let (n,a,b) = Scanf.scanf "%d %d %d\n" (fun x y z -> (x,y,z))

let pr x = print_endline (string_of_int x)

let (--) m n =
  let rec iter i res =
    if i >= m then iter (i - 1) (i::res)
    else res in
  let rec iter' i res =
    if i <= m then iter' (i + 1) (i::res)
    else res in
  if m <= n then iter n []
  else iter' n []

let digit_list_of_num n =
  let digit n = int_of_float (floor (log10 (float_of_int n))) in
  let base digit = int_of_float (10.0 ** (float_of_int digit)) in
  let rec iter rem res =
    let base = digit rem
              |> base in
    let top = rem / base in
    if base = 1 then top :: res
    else iter (rem - (top * base)) (top :: res) in
  iter n []

let digit_sum n =
  digit_list_of_num n
  |> List.fold_left (fun sum x -> x + sum) 0
    
let () = List.fold_left
           (fun sum x ->
             let ds = digit_sum x in
             if ds >= a && ds <= b then
               sum + x
             else sum) 0 (1--n)
         |> pr