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#include <iostream>
using namespace std;
int main()
{
	int i, n, k, counter = 0, wordsCounter = 0;
	bool noClosedBracket = false;
	bool addOne = false;
	bool isWord = false;
	cin >> n;
	cin >> k;

	int podzial = n / k;
	
	if (podzial < 2) {
		cout << "0";
		return 0;
	}
	k -= 1;
	char* tab = new char[n];
	int* div = new int[n];
	for (i = 0; i < n; i++) {
		cin >> tab[i];
	}

	for (int i = 0; i < n; i++) {
		counter++;
			if (i == n - 1) {
				podzial -= 2;
			}
		if (counter == podzial && k > 0) {
			div[i] = 1;
			counter = 0;
			k--;
		}
		else {
			div[i] = 0;
		}
	}
	for (i = 0; i < n - 1; i++) {
		if (isWord == true && tab[i] == ')' && noClosedBracket == false) {
			isWord = false;
		}

		if (noClosedBracket && tab[i] == ')' && div[i] == 0) {
			wordsCounter++;

			if (isWord) {
				wordsCounter++;
				isWord = false;
			}
			else {
				isWord = true;
			}
			noClosedBracket = false;
		}
		else {

			if (tab[i] == '(' && tab[i + 1] == ')' && div[i] == 0 && div[i + 1] == 0) {
				wordsCounter++;
				if (isWord) {
					wordsCounter++;
					isWord = false;
				}
				else {
					isWord = true;
				}
				i++;
			}
			else if (div[i] == 1) {
				noClosedBracket = false;
				addOne = false;
				isWord = false;
			}
			else if (div[i] == 0 && tab[i] == '(') {
				noClosedBracket = true;
				if (isWord) {
					addOne = true;
				}
			}
		}
	}
	if (noClosedBracket && tab[n] == ')') {
		wordsCounter++;
		isWord = true;
	}
	if (addOne) {
		wordsCounter++;
	}

	cout << wordsCounter;
}