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#include<cstdio>
#include<iostream>
#include<iomanip>
#include<algorithm>
#include<string>
#include<vector>
#include<cmath>
#include<stack>
#include<set>

using namespace std;

typedef vector<int> VI;
typedef long long LL;
typedef vector<LL> VLL;
typedef pair<int, int> PII;
typedef vector<PII> VPII;

#define FOR(x, b, e) for(int x=b; x<=(e); ++x)
#define FORD(x, b, e) for(int x=b; x>=(e); --x)
#define REP(x, n) for(int x=0; x<(n); ++x)
#define VAR(v, n) __typeof(n) v = (n)
#define ALL(c) (c).begin(), (c).end()
#define SIZE(x) ((int)(x).size())
#define FOREACH(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i)
#define PB push_back
#define ST first
#define ND second

int lsb(int x) {
    return x & -x;
}

struct FenwickPURQ {
    int size;
    VLL tab;

    FenwickPURQ(int n): size(n) {
        tab.resize(n + 1);
    }

    void add(int i, LL x) {
        i++;
        while (i <= size) {
            tab[i] += x;
            i += lsb(i);
        }
    }

    LL get(int l, int r) {
        return get(r) - get(l - 1);
    }

    LL get(int r) {
        r++;
        LL sum = 0;
        while (r > 0) {
            sum += tab[r];
            r -= lsb(r);
        }
        return sum;
    }
};

struct FenwickRUPQ {
    FenwickPURQ tree;

    FenwickRUPQ(int n): tree(FenwickPURQ(n)) {}

    void add_range(int l, int r, LL x) {
        tree.add(l, x);
        tree.add(r + 1, -x);
    }

    LL get(int r) {
        return tree.get(r);
    }
};

int main() {
	ios_base::sync_with_stdio(0);
    cin.tie(NULL); cout.tie(NULL);
    int n, k;
    cin >> n >> k;
    string s;
    cin >> s;
    FenwickRUPQ f(n);
    set<PII> ranges;
    REP(i, n) {
        stack<char> st;
        bool isOk = true;
        int j = i;
        while (j < n && isOk) {
            if (s[j] == '(') {
                st.push(s[i]);
            } else {
                if (st.empty()) isOk = false;
                else {
                    st.pop();
                    if (st.empty()) {
                        ranges.insert({i, j - 1});
                        f.add_range(i, j - 1, 1);
                    }
                }
            }
            j++;
        }
    }
    REP(j, k - 1) {
        PII best = {0, -1};
        if (ranges.empty()) break;
        REP(i, n) {
            LL tmp = f.get(i);
            if (tmp > best.ST) best = {tmp, i};
        }
        for (auto r = ranges.begin(); r != ranges.end();) {
            if ((*r).ST > best.ND) break;
            if (best.ND <= (*r).ND) {
                f.add_range((*r).ST, (*r).ND, -1);
                r = ranges.erase(r);
            } else ++r;
        }
    }
    cout << ranges.size() << '\n';
    return 0;
}