Problem:
Score : 200 points

Problem Statement

Given are two strings S and T.

Let us change some of the characters in S so that T will be a substring of S.

At least how many characters do we need to change?

Here, a substring is a consecutive subsequence. For example, xxx is a substring of yxxxy, but not a substring of xxyxx.

Constraints

The lengths of S and T are each at least 1 and at most 1000.

The length of T is at most that of S.

S and T consist of lowercase English letters.

Input

Input is given from Standard Input in the following format:

S
T

Output

Print the minimum number of characters in S that need to be changed.

Sample Input 1

cabacc
abc

Sample Output 1

1

For example, changing the fourth character a in S to c will match the second through fourth characters in S to T.

Since S itself does not have T as its substring, this number of changes - one - is the minimum needed.

Sample Input 2

codeforces
atcoder

Sample Output 2

6

Solution in OCaml (4.10.0) (judge verdict: Accepted)

open Core;;

let s = In_channel.(input_line_exn stdin)
let t = In_channel.(input_line_exn stdin)

let () = 
  let res =
    let n = String.length s in
    let m = String.length t in
    let dist x y =
      let rec cnt i = if (i < 0) then 0 else (if (Char.equal (String.get x i) (String.get y i)) then 0 else 1) + cnt (i - 1) in
      cnt ((String.length x) - 1)
    in
    List.range 0 (n - m + 1) |>
    List.map ~f:(fun i -> dist (String.sub ~pos:i ~len:m s) t) |>
    List.reduce_exn ~f:Int.min
  in
  printf "%d\n" res
;;