#include <iostream>
#include <string>


using namespace std;
//() )   (() ())()(())  ()()             ((| () ()) (() ()))  6, , (((| ) ()) (() ()))       () (() ()  (((| )

int Max(int n, int *value)
{
    int max = 0;
    int zwroc = 0;
    for (int i = 0; i < n; i++)
    {
        if (value[i] > max)
        {
            max = value[i];
            value[i] = 0;
            zwroc = i;
        }
    }
    return zwroc;
}

int NAW(int l, int r, string tab)
{
    bool byl=0;
    int amount = 0;
    int otwartyNawias = 0;
    int zaliczonyWyraz = 0;
    if (tab[l] == '(')
    {
        otwartyNawias++;
    }
    l++;
    //cout << "hello" << endl;
    //cout << "r+1 to: " << r+1<<endl;
    while (l != r+1)
    {
        if (otwartyNawias < 0)
            otwartyNawias = 0;

        if (zaliczonyWyraz < 0)
            zaliczonyWyraz = 0;

        /* if ((tab[l - 1] == '(' && tab[l] == ')') && ((l) != (r)))
         {
             amount++;
             if (counter>0)
             {
                 amount++;
                 counter--;
             }
             counter++;



             cout << "1 to  else if l to: " << l << endl<< " zmienna byl to: " << byl << endl << " amount to: " << amount << endl << " a counter to: " << counter << endl;
         }
         else if ((tab[l - 1] == '(' && tab[l] == '(') && ((l) != (r)))
         {
             counter++;

             cout << "2 else if l to: " << l << endl << " zmienna byl to: " << byl << endl << " amount to: " << amount << endl << " a counter to: " << counter << endl;
         }
         else if ((tab[l - 1] == ')' && tab[l] != '(') && (counter>0) && ((l) != (r)))
         {
             byl = 0;
             cout << "3 else to l to: " << l << endl << " zmienna byl to: " << byl << endl << " amount to: " << amount << endl << " a counter to: " << counter << endl;
             counter--;
         }
         else if ((tab[l - 1] == ')' && tab[l] == ')') && ((l) != (r)))
             counter--;


         l++;
     }*/

      if (tab[l - 1] == '(' && tab[l] == '(')
        {
            otwartyNawias++;
            //cout << "pierwszy if, otwartych nawiasow to: " << otwartyNawias << " amount to: " << amount << " zaliczonyWyraz " << zaliczonyWyraz << " L wynosi: " << l << endl;
        }
        else if (tab[l - 1] == '(' && tab[l] == ')')
        {
            amount++;
            otwartyNawias--;
            if (otwartyNawias > 0)
            {
                amount++;
            }
            zaliczonyWyraz++;
            //cout << "drugi if, otwartych nawiasow to: " << otwartyNawias << " amount to: " << amount << " zaliczonyWyraz " << zaliczonyWyraz << " L wynosi: " << l << endl;
        }
        else if (tab[l - 1] == ')' && tab[l] == ')' && otwartyNawias > 0)
        {
            amount++;
            otwartyNawias--;
            zaliczonyWyraz--;
           // cout << "trzeci if, otwartych nawiasow to: " << otwartyNawias << " amount to: " << amount << " zaliczonyWyraz " << zaliczonyWyraz << " L wynosi: " << l << endl;
        }
        else if (tab[l - 1] == ')' && tab[l] == '(')
        {
            /*amount++;

            if (zaliczonyWyraz > 0)
            {
                amount++;
                zaliczonyWyraz--;
            }
                otwartyNawias++;*/
            if (otwartyNawias > 0)
            {
                zaliczonyWyraz++;
                amount++;
            }
            otwartyNawias++;

           // cout << "czwarty if, otwartych nawiasow to: " << otwartyNawias << " amount to: " << amount << " zaliczonyWyraz " << zaliczonyWyraz << " L wynosi: " << l << endl;
        }
        else
        {
            zaliczonyWyraz = 0;
            otwartyNawias = 0;
        }
       //cout <<endl <<endl << "poza ifem otwartych nawiasow to: " << otwartyNawias << " amount to: " << amount << " zaliczonyWyraz " << zaliczonyWyraz << " L wynosi: " << l << endl;
       //cout << "tu skonczylem"<<endl;
       l++;
      // cout << "r+1 to: " << r + 1 << endl;
      // cout << "a l to: " << l << endl;
    }



    return amount;
}
int main()
{
    int n, k;

    char otw = '(';
    char zam = ')';

    int temp1 = 0;
    int sum=0;

    cin >> n;
    cin >> k;

    string tab;
    
    int* pomoc = new int[n];

    cin >> tab;

    int* pom = new int[k+1];
    pom[0] = 0;
    for (int i = 1; i < k; i++)
        pom[i] = 0;

    pom[k] = n-1;

    for(int i = 0; i<n; i++)
    {
        pomoc[i] = 0;
    }

    for (int i = 0; i < n; i++)
    {
        if (tab[i] == otw)
        {
            temp1++;
        }
        else if(tab[i] == zam && i>0 && temp1 != 0)
        {
            pomoc[i-1] = temp1;
            temp1 = 0;
        }
    }
    
    //for (int i = 0; i < k + 1; i++)
    //{
    //    cout << "przedprzed i to:" << i << "wwartosc to: " << pom[i] << endl;
    //}

    for (int i = 1; i < k; i++)
    {
        pom[i] = Max(n, pomoc);
    }
    
    //for (int i = 0; i < k + 1; i++)
    //{
    //    cout << "przed i to:" << i << "wwartosc to: " << pom[i] << endl;
    //}

    for (int i = 0; i < k; i++)
    {
        for (int j = 0; j < k; j++)
        {
            if (pom[j] > pom[j + 1])
                swap(pom[j], pom[j + 1]);
        }
    }
    int i = 0;
//    tak wyglada tablica
    for (i = 0; i<k; i++)
    {
     //   cout << "i to:" <<i<< "wwartosc to: "<< pom[i] << endl;
        if (pom[i + 1] > 0)
        {
            pom[i] = -1;
            break;
        }
    }

    bool lec = 1;

    for (i = 0; i < k+1; i++)
    {
        if (pom[i] == 0)
        {
            lec = 0;
        }
    }

   /* for (int i = 0; i < k + 1; i++)
    {
        cout << "po i to:" << i << "wwartosc to: " << pom[i] << endl;
    }*/

    if (lec)
    {
        for (i=0; i < k; i++)
        {
            sum += NAW(pom[i] + 1, pom[i + 1], tab);
        }
    }

    cout << sum;
    

}