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#include <iostream>
#include <vector>
#include <deque>
#include <algorithm>
#include <limits>
using namespace std;
const long long INF = numeric_limits<long long>::max() / 2;

struct SuffixContainer {
    deque<int>dq{1};
    long long good = 0;

    void shift_plus() {
        dq.push_front(1);
    }

    void shift_minus() {
        dq.pop_front();
        if (dq.empty())
            dq.push_front(0);
        good += dq.front();
        dq.front()++;
    }

    int get_good() const {
        return good;
    }
};

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, k;
    string s;
    cin >> n >> k >> s;

    // find interesting points
    vector<int>Interest;
    for (int i = 1; i < n; i++)
        if (s[i-1] == '(' && s[i] == ')')
            Interest.push_back(i);

    if ((int)Interest.size() < k) {
        cout << "0\n";
        return 0;
    }

    // make dp over interestiong points
    vector<vector<long long>>dp;
    vector<SuffixContainer>SC;

    dp.push_back(vector<long long>(k));
    dp[0][0] = 0;
    for (int i = 1; i < k; i++)
        dp[0][i] = INF;
    SC.push_back(SuffixContainer());

    int char_it = 0;
    for (int ip = 0; ip < (int)Interest.size(); ip++) {
        /* int ileft = Interest[ip] - 1; */
        int iright = Interest[ip];

        // update suffixes
        while (char_it < iright) {
            for (auto& sc : SC)
                if (s[char_it] == '(')
                    sc.shift_plus();
                else
                    sc.shift_minus();
            char_it++;
        }

        // calculate dp
        vector<long long> newcol(k);
        newcol[0] = INF;
        for (int kk = 1; kk < k; kk++) {
            newcol[kk] = INF;
            for (int i = dp.size() - 1; i >= 0 && newcol[kk] >= SC[i].get_good(); i--)
                newcol[kk] = min(newcol[kk], dp[i][kk-1] + SC[i].get_good());
        }

        // add to structures
        dp.push_back(move(newcol));
        SC.push_back(SuffixContainer());
    }

    // choose the best solution
    while (char_it < n) {
        for (auto& sc : SC)
            if (s[char_it] == '(')
                sc.shift_plus();
            else
                sc.shift_minus();
        char_it++;
    }

    long long result = INF;
    for (int i = 0; i <= (int)Interest.size(); i++)
        result = min(result, dp[i][k-1] + SC[i].get_good());
    cout << result << "\n";


    return 0;
}