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#include <iostream>
#include <map>
#include <stack>
#include <string>
#include <unordered_map>

typedef long long int i64;

const i64 INF = 1LL << 60;

using std::string;

template <typename T> T min_of(T a, T b) { return a < b ? a : b; }
template <typename T> T max_of(T a, T b) { return a > b ? a : b; }

class Processor {
  i64 nawness;
  std::stack<i64> st;
  i64 at_level;
  int last;

public:
  inline i64 _nawness() { return nawness; }

  Processor() : nawness(0), at_level(1), last(-1) {}

  i64 process(char c, int idx) {
    if (idx == last) {
      return _nawness();
    }
    last = idx;
    if (c == '(') {
      st.push(at_level);
      at_level = 1;
    } else if (!st.empty()) {
      at_level = st.top();
      st.pop();
      nawness += at_level;
      at_level += 1;
    } else {
      at_level = 1;
    }

    return nawness;
  }
};

i64 find_min(string &word, int start, int k, i64 budget) {

  static std::unordered_map<i64, i64> cache;
  i64 key = (i64)start << 32 | k;
  auto res = cache.find(key);
  if (res != cache.end()) {
    return res->second;
  }

  Processor proc;
  int end = word.length();
  if (k == 0) {
    for (int i = start; i < end; ++i) {
      proc.process(word[i], i);
    }
    return cache[key] = proc._nawness();
  } else {
    i64 min = INF;
    i64 rest = 0;
    i64 used = 0;
    for (int i = start; i < end; ++i) {
      while (proc.process(word[i], i) == used) {
        if (++i == end || used > budget || used >= min) {
          if (min == INF) {
            return cache[key] = 0;
          } else {
            return cache[key] = min;
          }
        }
      }
      --i;

      rest = find_min(word, i + 1, k - 1, budget);
      min = min_of(min, used + rest);
      used = proc._nawness();
    }
    return cache[key] = min;
  }
}

int main() {
  int K;
  string word;
  std::cin >> K >> K;
  std::cin >> word;

  int right = 0;
  for (char c : word) {
    if (c == ')') {
      ++right;
    }
  }

  i64 len = ((word.length() / K) + 5 ) / 2;
  i64 budget = len * (len + 1) / 2;

  std::cout << find_min(word, 0, K - 1, budget) << "\n";

  return 0;
}