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#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <map>
#include <set>
#include <chrono>
#include <functional>
#include <cstdlib>
#include <cassert>
#include <sstream>
#include <climits>
using namespace std;


struct Elem
{
  int height = 0;
  int count = 0;
};

struct NawiasowoscInfo
{
  long long minnawiasowosc = 0;
  int maxLeftPodzial = 0;
};

int main()
{
  //ios::sync_with_stdio(false);
  //std::cin.ignore(256, '\n');
  const clock_t begin_time = clock();
  int n;
  int k;
  std::cin >> n >> k;
  k--;

  std::string nawiasy;
  std::cin >> nawiasy;

  std::vector<int> peaks;
  std::vector<int> ext_peaks;
  ext_peaks.push_back(0);
  for (int i = 0; i < nawiasy.size() - 1; ++i)
  {
    if (nawiasy[i] == '(' && nawiasy[i+1] == ')')
    {
      peaks.push_back(i+1);
      ext_peaks.push_back(i+1);
    }
  }
  if (peaks.size() <= k)
  {
    std::cout << "0\n";
    return 0;
  }
  std::vector<std::vector<long long>> nawiasowosc(nawiasy.size());
  for (int i=0; i< ext_peaks.size(); ++i)
  {
    int start = ext_peaks[i];
    nawiasowosc[start].resize(nawiasy.size()+1);
    std::vector<Elem> elements;
    int height = 0;
    long long count = 0;
    elements.push_back({height, 1 });
    for (int j = start; j < nawiasy.size(); ++j)
    {
      if (nawiasy[j] == '(')
      {
        height++;
        elements.push_back({height, 1});
      }
      else
      {
        height--;
        if (elements.size() > 0)
        {
          elements.pop_back();
        }
        if (elements.size() > 0)
        {
          count += elements.back().count;
          ++elements.back().count;
        }
        else
        {
          elements.push_back({ height, 1 });
        }
      }
      nawiasowosc[start][j + 1] = count;
    }
  }
  
  ext_peaks.push_back(nawiasy.size());
  std::vector<std::vector<NawiasowoscInfo>> table(ext_peaks.size());
  for (int ni = 0; ni < ext_peaks.size(); ++ni)
  {
    table[ni].resize(k+1);
    table[ni][0].minnawiasowosc = nawiasowosc[0][ext_peaks[ni]];
    table[ni][0].maxLeftPodzial = 0;
  }
  for (int ki = 1; ki <= k; ++ki)
  {
    table[0][ki].minnawiasowosc = 0;
    table[0][ki].maxLeftPodzial = 0;
    for (int ni = 1; ni < ext_peaks.size(); ++ni)
    {
      int lastPodzial = table[ni-1][k].maxLeftPodzial;
      long long minNawiasowosc = LLONG_MAX;
      int bestPodzial;
      for (int p = lastPodzial; p < ni; ++p)
      {
        long long nawias = table[p][ki-1].minnawiasowosc + nawiasowosc[ext_peaks[p]][ext_peaks[ni]];
        if (nawias <= minNawiasowosc)
        {
          minNawiasowosc = nawias;
          bestPodzial = p;
        }
      }
      table[ni][ki].minnawiasowosc = minNawiasowosc;
      table[ni][ki].maxLeftPodzial = bestPodzial;
    }
  }
  std::cout << table[ext_peaks.size()-1][k].minnawiasowosc << "\n";


  //std::vector<std::vector<long long>> 

  //testMaxTest();
  //testBigNumbers();
  //testFractions();
  //std::cout << float(clock() - begin_time) / CLOCKS_PER_SEC << "\n";
  return 0;
};