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#include <bits/stdc++.h> 

typedef long long int lli;

using namespace std;

#define MAX3 1010
#define MAX4 10010
#define MAX5 100010
#define MAX6 1000010

template <typename T >
void dbg(T last)
{
  cout << last << "\n";
}

template <typename T, typename ...args>
void dbg(T current, args ...next)
{
  cout << current << ' ';
  dbg(next...);
}

/*************************************************/
int n,k;
char tab[MAX6];
int dp[4003][4003];
int dp2[4003][4003];


int getHowMany(int l, int p)
{
  int ans = 0;
  int diff = 0;
  if (dp2[l][p] != -1)
  {
    return dp2[l][p];
  }
  for (int i =l;i<=p;i++)
  {
    // dbg("znak", i, tab[i]);
    diff = 0;
    if (tab[i] == '(')
    {
      diff++;
      for (int j=i+1;j<=p;j++)
      {
        diff += (tab[j] == '('? 1 : -1);
        // dbg(j, tab[j], diff);
        if (diff == 0)
        {
          ans++;
        }
        if (diff < 0)
        {
          break;
        }
      }
    }
  }

  // dbg("how many", l ,p, ans);
  dp2[l][p] = ans;
  return ans;
}

lli calc(int x, int d)
{
  lli ans = INT_MAX;
  // dbg("calc od:", x, d);
  if (n-x < d)
  {
    return ans;
  }
  if (dp[x][d] != -1)
  {
    return dp[x][d];
  }

  if (d == 0)
  {
    return getHowMany(x,n);
  }

  for (int i=x;i<=n;i++)
  {
    lli uu = calc(i+1, d-1);
    lli uu2 = getHowMany(x, i);
    // dbg("tmp ", uu, uu2);
    ans = min(ans, uu + uu2);
  }

  dp[x][d] = ans;
  // dbg("wynik: ", x, d, ans);
  return ans;
}

void solve()
{
  cin >> n >> k;

  for (int i=1;i<=n;i++)
  {
    cin >> tab[i];
  }

  for (int i=0;i<=n;i++)
  {
    for (int j=0;j<=n;j++)
    {
      dp[i][j] = -1;
      dp2[i][j] = -1;
    }
  }

  cout << calc(1,k-1);
  cout << "\n";
}

int main()
{
  std::ios::sync_with_stdio(false);

  solve();

  return 0;
}


/*

15 2
())(()())()(())

4 2
()()

15 3
())(()())()(())

*/