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#include <bits/stdc++.h>
using namespace std;

using T = unsigned;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int n, k; cin >> n >> k;
    if (n < 3) {
        cout << 0 << endl;
        return 0;
    }
    string word; cin >> word;
    vector<int> maxPos;
    unordered_map<int, int> maxes;
    maxes[0] = 0;
    maxPos.push_back(0);
    for (int i = 0, cnt = 1; i < n; ++i) {
        if (i == n - 1) {
            maxes[n] = cnt++;
            maxPos.push_back(n);
            continue;
        }
        if (word[i] == '(' and word [i + 1] == ')') {
            maxes[i + 1] = cnt++;
            maxPos.push_back(i + 1);
        }
    }
    if (k >= size(maxPos) - 1) {
        cout << 0 << endl;
        return 0;
    }
    vector<vector<T>> h(size(maxes));
    for (auto &l : h) l.resize(size(maxes));
    for (auto startPos : maxPos) {
        stack<int> s;
        s.push(1);
        T acc{};
        for (int i = startPos; i < n; ++i) {
            if (i > 0 and word[i - 1] == '(' and word[i] == ')') h[maxes[startPos]][maxes[i]] = acc;
            if (word[i] == '(') {
                s.push(1);
            } else {
                s.pop();
                if (s.empty()) s.push(0);
                acc += s.top();
                ++s.top();
            }
        }
        h[maxes[startPos]][maxes[n]] = acc;
    }
    vector<vector<pair<T, int>>> dp(k);
    for (auto &dpp : dp) dpp.resize(size(maxPos), {0, 1});

    for (int nn = 1; nn < size(dp[0]); ++nn) {
        for (int kk = 1; kk <= size(dp); ++kk) {
            if (kk == 1) {
                dp[0][nn] = {h[0][nn], 1};
                continue;
            }
            T acc = numeric_limits<T>::max();
            int best = kk - 1;
            for (int tmp = dp[kk - 2][nn - 1].second; tmp < nn; ++tmp) {
                T x = dp[kk - 2][tmp].first + h[tmp][nn];
                if (x <= acc) {
                    acc = x;
                    best = tmp;
                }
            }
            dp[kk - 1][nn] = {acc, best};
        }
    }
    cout << dp.back().back().first << endl;
    return 0;
}