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#include <bits/stdc++.h>

using namespace std;

int INF = numeric_limits<int>::max();

int length, groups;
string word;
vector<int> maxs;
vector<vector<int>> ranges;
vector<vector<pair<int, int>>> dp;

void read() {
    cin >> length >> groups;
    cin >> word;
}

void findMaxs() {
    for (int i = 0; i < length - 1; ++i) {
        if (word[i] == '(' && word[i + 1] == ')') {
            maxs.push_back(i + 1);
        }
    }
}

void computeRangesForStart(int index) {
    stack<int> stack;
    stack.push(1);
    vector<int> row;
    int result = 0;
    int maxIndex = index;
    int start = (index == 0) ? 0 : maxs[index-1];

    for (int i = start; i < length; ++i) {
        if (word[i] == '(') {
            stack.push(1);
        } else {
            if (!stack.empty()) {
                stack.pop();
            }
            if (!stack.empty()) {
                result += stack.top();
                stack.top()++;
            } else {
                stack.push(1);
            }
        }
        if (i == maxs[maxIndex] - 1 || i == length - 1) {
            row.push_back(result);
            maxIndex++;
        }
    }
    ranges.push_back(row);
}

void computeRanges() {
    for (int i = 0; i <= maxs.size(); ++i) {
        computeRangesForStart(i);
    }
}

void dynamic() {
    for (int i = 0; i < groups; ++i) {
        vector<pair<int, int>> row;
        dp.push_back(row);
    }
    for (int i = 0; i <= maxs.size(); ++i) {
        for (int j = 0; j < groups; ++j) {
            if (j > i) {
                dp[j].emplace_back(INF, 0);
            } else if (i == 0) {
                dp[j].emplace_back(0, 0);
            } else if (j == 0) {
                dp[j].emplace_back(ranges[0][i], 0);
            } else {
                int sum = INF, index = dp[j][i - 1].second;
                for (int k = index; k < i; ++k) {
                    if (dp[j - 1][k].first < INF) {
                        int current = dp[j - 1][k].first + ranges[k + 1][i - k - 1];
                        if (current <= sum) {
                            sum = current;
                            index = k;
                        }
                    }
                }
                dp[j].emplace_back(sum, index);
            }
        }
    }
}

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

    read();
    findMaxs();
    if (maxs.size() < groups) {
        cout << 0 << endl;
        return 0;
    }

    computeRanges();
    dynamic();
    cout << dp[groups - 1][maxs.size()].first << endl;


    return 0;
}