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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;


void solve(std::string S, std::string T){
  ll Ss = (ll) S.size();
  ll Ts = (ll) T.size();
  ll inf = Ss+1;
  vector<ll> dp((Ss+1) * (Ts+1), inf);
  const auto ix = [Ts](ll i, ll j) {
    return i * (Ts+1) + j;
  };
  for (ll i = 0; i <= Ss; ++i) {
    dp[ix(i, 0)] = 0;
  }
  for (ll j = 1; j <= Ts; ++j) {
    for (ll i = 1; i <= Ss; ++i) {
      if (dp[ix(i-1,j-1)] < inf) {
        dp[ix(i, j)] = dp[ix(i-1, j-1)] + (S[i-1] != T[j-1]);
      }
    }
  }
  ll rv = inf;
  for (ll i = 0; i < Ss; ++i) {
    rv = min(rv, dp[ix(i, Ts)]);
  }
  cout << rv << endl;
}

int main() {
  std::string S;
  std::cin >> S;
  std::string T;
  std::cin >> T;
  solve(S, T);
  return 0;
}