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#include <bits/stdc++.h>

using namespace std;

const size_t INF = numeric_limits<size_t>::max();

struct TestCase
{
  size_t n, k;
  string s;
};

TestCase read_test_case();
void solve_test_case(const TestCase&);

int main()
{
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  solve_test_case(read_test_case());
}

TestCase read_test_case()
{
  TestCase tc;
  cin >> tc.n >> tc.k >> tc.s;
  return tc;
}

void solve_test_case(const TestCase& tc)
{
  vector<vector<size_t>> dp(tc.n + 1, vector<size_t>(tc.k + 1, INF));
  dp[tc.n][0] = 0;

  for (int begin = tc.n - 1; begin >= 0; begin--)
  {
    size_t score = 0;
    stack<size_t> s;
    for (size_t j = begin; j < tc.n; j++)
    {
      if (tc.s[j] == '(')
        s.push(0);
      else if (tc.s[j] == ')' && !s.empty())
      {
        // pop content of closed paren
        while (!s.empty() && s.top() > 0) s.pop();

        // found closing brace
        if (!s.empty())
        {
          s.pop();  // Pop (

          // Add 1 to current sequence of parens
          if (!s.empty() && s.top() > 0)
            s.top()++;
          else
            s.push(1);
        }

        if (!s.empty()) score += s.top();
      }

      for (size_t k = 1; k <= tc.k; k++)
        if (dp[j + 1][k - 1] != INF)
          dp[begin][k] = min(dp[begin][k], dp[j + 1][k - 1] + score);
    }
  }

  cout << dp[0][tc.k] << "\n";
}