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// fajne zadanko, ale glupio ze da sie zgadnac wynik xD
#include <bits/stdc++.h>
using namespace std;
using LL = long long;
#define e1 first
#define e2 second
#define pb push_back
#define OUT(x) {cout << x << "\n"; exit(0); }
#define TCOUT(x) {cout << x << "\n"; return; }
#define FOR(i, l, r) for(int i = (l); i <= (r); ++i)
#define rep(i, l, r) for(int i = (l); i < (r); ++i)
#define boost {ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); }
#define sz(x) int(x.size())
#define trav(a, x) for(auto& a : x)
#define all(x) begin(x), end(x)
typedef long long ll;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;
mt19937_64 rng(time(0));
int random(int l, int r) {
	return uniform_int_distribution<int>(l, r)(rng);
}
#ifdef DEBUG
template<class T> int size(T &&x) {
	return int(x.size());
}
template<class A, class B> ostream& operator<<(ostream &out, const pair<A, B> &p) {
	return out << '(' << p.first << ", " << p.second << ')';
}
template<class T> auto operator<<(ostream &out, T &&x) -> decltype(x.begin(), out) {
	out << '{';
	for(auto it = x.begin(); it != x.end(); ++it)
		out << *it << (it == prev(x.end()) ? "" : ", ");
	return out << '}';
}
void dump() {}
template<class T, class... Args> void dump(T &&x, Args... args) {
	cerr << x << ";  ";
	dump(args...);
}
#endif
#ifdef DEBUG
  struct Nl{~Nl(){cerr << '\n';}};
# define debug(x...) cerr << (strcmp(#x, "") ? #x ":  " : ""), dump(x), Nl(), cerr << ""
#else
# define debug(...) 0 && cerr
#endif

const int maxn = 7001;

int koszt[maxn][maxn];
bitset <maxn> jest[maxn];
struct DP {
	int n; vi dp;
	vector<pii> res;
	DP(int n, vi dp) : n(n), dp(dp), res(n, {0, INT_MAX}) {}
	
	int lo(int i) { return 0; }
	int hi(int i) { return i + 1; }
	ll f(int i, int j) { return koszt[i][j] + (i > 0 ? dp[i - 1] : 0); }
	void store(int i, int j, ll v) { res[i] = {j, v}; }

	void rec(int L, int R, int LO, int HI) {
		if (L >= R) return;
		int mid = (L + R) >> 1;
		pair<ll, int> best(LLONG_MAX, LO);
		rep(k, max(LO,lo(mid)), min(HI,hi(mid)))
			best = min(best, make_pair(f(k, mid), k));
		store(mid, best.second, best.first);
		rec(L, mid, LO, best.second+1);
		rec(mid+1, R, best.second, HI);
	}
	vi solve(int L, int R) { 
		rec(L, R, INT_MIN, INT_MAX);
		vi ret(R - L, 0);
		rep(i, L, R) ret[i] = res[i].second;
		return ret;
	}
};

int main() {
	boost;
	int n, k;
	cin >> n >> k;
	string s;
	cin >> s;
	vi vec(n);
	rep(i, 0, n) vec[i] = (s[i] == '(') ? 1 : -1;
	
	rep(L, 0, n) {
		int ile = 0;
		int minn = 0;
		rep(R, L, n) {
			ile += vec[R];
			minn = min(minn, ile);
			int ten = (ile == 0 && minn >= 0) ? 1 : 0;
			jest[L].set(R, ten);
		}
	}
	rep(L, 0, n) koszt[L][L] = 0;
	FOR(len, 2, n) {
		rep(L, 0, n - len + 1) {
			int R = L + len - 1;
			koszt[L][R] = koszt[L+1][R] + koszt[L][R - 1] - koszt[L + 1][R - 1] + jest[L][R];
		}
	}
	
	vi wynik(n, 0);
	rep(i, 0, n) wynik[i] = koszt[0][i];
	rep(step, 1, k) {
		DP solver(n, wynik);
		wynik = solver.solve(0, n);
	}
	
	cout << wynik[n - 1] << "\n"; 	
}