bool M1;
#include<iostream>
#include<algorithm>
#include<cstring>
#include<cstdlib>
#include<climits>
#include<iomanip>
#include<cassert>
#include<random>
#include<cstdio>
#include<vector>
#include<bitset>
#include<stack>
#include<queue>
#include<deque>
#include<cmath>
#include<ctime>
#include<map>
#include<set>
//#include<ext/pb_ds/assoc_container.hpp>
//#include<ext/pb_ds/hash_policy.hpp>
//#include<ext/pb_ds/priority_queue.hpp>
#define fi first
#define se second
#define ll long long
#define Vector Point
#define I128 __int128
#define LD long double
#define ull unsigned ll
#define pii pair<ll,int>
#define pb(x) push_back(x)
#define syt cerr<<"sytakioi\n"
#define F(i,a,b) for(int i=a,i##end=b;i<=i##end;++i)
#define UF(i,a,b) for(int i=a,i##end=b;i>=i##end;--i)
#define look_memory cerr<<abs(&M2-&M1)/1024.0/1024<<'\n'
#define rd_i(l,r) uniform_int_distribution<int>(l,r)(rd)
#define rd_r(l,r) uniform_real_distribution<double>(l,r)(rd)
#define look_time cerr<<(clock()-Time)*1.0/CLOCKS_PER_SEC<<'\n'
using namespace std;
//using namespace __gnu_cxx;
mt19937 rd(time(0));
const int N=1e6+5;
int n,h,t,ans;
char c[N];
bool M2;
signed main(){
	int Time=clock();
	look_memory;
	cin.tie(nullptr)->sync_with_stdio(false);
	cin>>n>>h>>(c+1);
	F(i,1,n){
		if(c[i]=='(') ++t;
		else --t;
		if(t>h) t-=2,++ans;
		if(t<0) t+=2,++ans;
	}
	cout<<ans<<'\n';
	look_time;
	return 0;
}