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#include <bits/stdc++.h>
using namespace std;
//{
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define FORD(i, a, b) for(int i = (a); i >= (b); --i)
#define VAR(v, i) __typeof(i) v=(i)
#define all(v) (v).begin(),(v).end()
#define FORE(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i)


#define PII pair<int,int>
#define st first
#define nd second
#define pb push_back
#define lint long long int
#define VI vector<int>

#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
  enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
  ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
  *this << "[";
  for (auto it = d.b; it != d.e; ++it)
	*this << ", " + 2 * (it == d.b) << *it;
  ris << "]";
}
};
//{
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "

#define make( x) int (x); scanf("%d",&(x));
#define make2( x, y) int (x), (y); scanf("%d%d",&(x),&(y));
#define make3(x, y, z) int (x), (y), (z); scanf("%d%d%d",&(x),&(y),&(z));
#define make4(x, y, z, t) int (x), (y), (z), (t); scanf("%d%d%d%d",&(x),&(y),&(z),&(t));
#define makev(v,n) VI (v); FOR(i,0,(n)) { make(a); (v).pb(a);} 
#define IOS ios_base::sync_with_stdio(0)
#define HEAP priority_queue

#define read( x) scanf("%d",&(x));
#define read2( x, y) scanf("%d%d",&(x),&(y));
#define read3(x, y, z) scanf("%d%d%d",&(x),&(y),&(z));
#define read4(x, y, z, t) scanf("%d%d%d%d",&(x),&(y),&(z),&(t));
#define readv(v,n) FOR(i,0,(n)) { make(a); (v).pb(a);}
#define jeb() fflush(stdout);
//}

int n, k;
char s[100005];

VI v;
vector<int> cost[100005];

void redukuj() {
	int pocz = 0;
	int kon = n-1;
	while (pocz < n && s[pocz] ==')') pocz++;
	while (kon >= 0 && s[kon] =='(') kon--;
	if (pocz > kon) return;
	int cnt = 1;
	int sgn = 1;
	FOR(i,pocz+1,kon+1) {
		if (s[i] == s[i-1]) cnt++;
		else {
			v.pb(cnt*sgn);
			sgn = -sgn;
			cnt = 1;
		}
	}
	v.pb(cnt*sgn);
}

int dp[100005][2];

void calculate_dp(int cur, int L, int R, int optL, int optR) {
		if (L >= R) return;
		int M = (L+R)/2;

		int best = dp[M-1][1-cur];
		int myopt = M;
		for (int j2 = min(M-1,optR); j2 >= max(1,optL); j2--) {
			best = min(best, dp[j2-1][1-cur] + cost[j2+1][M-(j2+1)]);
			if (best == dp[j2-1][1-cur] + cost[j2+1][M-(j2+1)]) {
				myopt = j2;
			}
		}
		if (optL == 0) {
			best = min(best, cost[1][M-1]);
			if (best == cost[1][M-1]) {
				myopt = 0;
			}
		}
		dp[M][cur] = best;

		calculate_dp(cur, L, M, optL, myopt);
		calculate_dp(cur, M+1, R, myopt, optR);


}

int main() {
	read2(n, k);
	scanf("%s", s);
	redukuj();
	//debug() << imie(v);
	if (v.size()/2 < k) {
		printf("0\n");
		return 0;
	}
	int K = v.size() / 2;
	
	FOR(i,0,K) {
		vector<PII> sklad;
		sklad.pb({0,1});
		sklad.pb({v[2*i],1});
		int ans = 0;
		FOR(j,2*i+1,v.size()) {
			if (j % 2 == 1) {
				int cur = sklad.back().st;
				int ncur = sklad.back().st + v[j];
				sklad.pop_back();
				while (sklad.size() > 0 && sklad.back().st > ncur) {
					ans += cur - sklad.back().st-1;
					ans += sklad.back().nd;
					cur = sklad.back().st;
					sklad.pop_back();
				}
				if (sklad.size() > 0 && sklad.back().st == ncur) {
					ans += cur - sklad.back().st-1;
					ans += sklad.back().nd;
					
					sklad[sklad.size()-1] = {sklad.back().st, sklad.back().nd + 1};
				} else if (sklad.size() > 0) {
					ans += cur - ncur;
					sklad.pb({ncur,2});
				}
				cost[i].pb(ans);
			} else {
				if (sklad.size() > 0) {
					int cur = sklad.back().st;
					cur += v[j];
					sklad.pb({cur,1});
				} else {
					sklad.pb({0,1});
					sklad.pb({v[j],1});
				}
			}
		}
	}
	/*FOR(i,0,K) {
		debug() << imie(cost[i]);
	}
	*/
	
	FOR(i,0,K) {
		dp[i][0] = cost[0][i];
	}
	/*FOR(i,0,K) cout << dp[i][0] << " ";
	cout << endl;*/
	int cur = 1;
	FOR(i,1,k) {
		dp[0][cur] = 0;
		calculate_dp(cur, 1, K, 0, K-1); 
		/*FOR(j,0,K) cout << dp[j][cur] << " ";
		cout << endl;*/
		cur = 1-cur;
	}
	printf("%d\n", dp[K-1][1-cur]);
}