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#include <cstdio>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <unordered_map>
using namespace std;

const int N = 100000 + 9;
int n;
int k;
char s[N];

vector<vector<int> > cnt;

int diff(char c) { return c == '(' ? 1 : -1; }

int max0[N];

map<pair<int, int>, int > mem;
int solve(int i, int k) {
	if (i <= max0[k]) return 0;
	if (1 == k) return cnt[0][i];
	pair<int, int> p{i, k};
	if (mem.count(p) > 0) return mem[p];
	int best = 999999999;
	for (int j=max0[k-1]+1; j<i; ++j) {
		int cur = solve(j - 1, k - 1) + cnt[j][i - j];
		if (cur < best) best = cur;
	}
	mem[p] = best;
	return best;
}

int main() {
	scanf("%d%d%s", &n, &k, s);
	cnt.resize(n);

	for (int i=0; i<n; ++i) {
		cnt[i].push_back(0);
		unordered_map<int, vector<int> > um;
		um[0].push_back(i - 1);
		int lvl = diff(s[i]);
		um[lvl].push_back(i);
		for (int j=i+1; j<n; ++j) {
			lvl += diff(s[j]);
			int add = 0;
			if (um.count(lvl - 1) == 0) {
				add = um[lvl].size();
			} else {
				int x = um[lvl - 1].back();
				vector<int> &v = um[lvl];
				int a = -1;
				int b = v.size();
				while (a + 1 < b) {
					int c = (a + b) / 2;
					if (v[c] < x)
						a = c;
					else
						b = c;
				}
				add = v.size() - b;
			}
			add += cnt[i].back();
			cnt[i].push_back(add);
			um[lvl].push_back(j);
		}
	}

	int st = 0;
	for (int x=1; x<=k; ++x) {
		int en = st;
		while (en < n && cnt[st][en - st] == 0) ++en;
		max0[x] = en - 1;
		st = en;
	}

	int res = solve(n - 1, k);
	printf("%d\n", res);

	return 0;
}