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#include <algorithm>
#include <array>
#include <cassert>
#include <cstdio>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <ranges>
#include <set>
#include <stack>
#include <string>
#include <vector>

using namespace std;

typedef long long LL;
#define int LL

typedef pair<int, int> PII;
const int INF = 1e18;

#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()

int n, kk;
string s;

vector<vector<int>> cost;

/*
vector<vector<int>> memo_f;

int f(int i, int j) {
    if (i < 0) return -INF;
    if (j < 0) return i == 0 ? 0 : -INF;

    int &res = memo_f[i][j];
    if (res != -1) return res;
    res = INF;
    for (int k = 0; k <= j; k++) {
        int v = f(i - 1, k - 1);
        if (v == -INF) continue;
        res = min(res, cost[k][j] + f(i - 1, k - 1));
    }
    return res;
}*/

struct S {
    int l, r;
    bool broken;
    S(int _l, int _r, bool _broken = false) : l(_l), r(_r), broken(_broken){};
};

vector<vector<S>> lists;

vector<vector<int>> match_memo;

int match(int i, int sum) {
    if (i == s.size()) return INF;
    if (sum < 0) return INF;
    int &res = match_memo[i][sum];
    if (res != -1) return res;
    sum += s[i] == '(' ? 1 : -1;
    if (sum == 0) return i;
    return res = match(i + 1, sum);
}

void parsed(vector<S> list) {
    if (!list.empty()) lists.push_back(list);
}

void parse(int l, int r) {
    assert(l < r);

    vector<S> list;
    while (true) {
        while (l < r && s[l] != '(') {
            list.push_back({S(l, l, true)});
            l++;
        }
        if (l == r) break;

        assert(s[l] == '(');
        int j;
        for (j = l; j < r; j++) {
            if (s[j] == '(' && match(j, 0) < r) {
                while (l < j) {
                    list.push_back({S(l, l, true)});
                    l++;
                }
                l = j;
                j = match(j, 0);
                break;
            }
        }

        if (j == r) break;
        assert(s[j] == ')');

        list.push_back(S(l, j));

        if (j != l + 1) parse(l + 1, j);

        l = j + 1;
    }
    parsed(list);
}
vector<vector<int>> dpf;

void huj(int g, int i, int j, int l, int r) {
    if (i > j) return;
    int mid = (i + j) / 2;
    int best = l;
    for (int k = l; k <= min(r, mid); k++) {
        int val = dpf[g - 1][k - 1] + cost[k - 1][mid - 1];
        if (val < dpf[g][mid]) {
            dpf[g][mid] = val;
            best = k;
        }
    }
    huj(g, i, mid - 1, l, best);
    huj(g, mid + 1, j, best, r);
}

int dupa(int k, int n) {
    n++;
    k++;
    dpf.resize(k + 1);
    for (auto &x : dpf) {
        x.resize(n + 1);
        for (auto &y : x) y = INF;
    }

    for (int i = 0; i <= k; i++) dpf[i][0] = i == 0;
    for (int j = 0; j <= n; j++) dpf[0][j] = INF;

    for (int i = 1; i <= k; i++) huj(i, 1, n, 1, n);

    return dpf[k][n];
}
int solve() {
    cost.resize(n);
    for (auto &x : cost) {
        x.resize(n + 1);
        for (auto &y : x) y = 0;
    }

    match_memo.resize(n);
    for (auto &x : match_memo) {
        x.resize(n + 1);
        for (auto &y : x) y = -1;
    }

    /*memo_f.resize(kk + 1);
    for (auto &x : memo_f) {
        x.resize(n + 1);
        for (auto &y : x) y = -1;
    }*/

    parse(0, n);

    for (int i = 0; i < n; i++) {
        for (auto &x : lists) {
            int count = 0;
            for (auto &y : x) {
                if (y.l < i) continue;
                if (y.broken) {
                    count = 0;
                    continue;
                }
                count++;
                cost[i][y.r] += count - 1;
                cost[i][y.r]++;
            }
        }
        for (int j = i + 1; j < n; j++) cost[i][j] += cost[i][j - 1];
    }

    return dupa(kk, n - 1);

    //  return f(kk, n - 1);
}

int solve2() {
    cin >> n >> kk;
    cin >> s;
    n = s.size();

    return solve();
}

#undef int
int main() {
    ios::sync_with_stdio(false);
    cin.exceptions(cin.failbit);
    cin.tie(0);
    cout << solve2() << "\n";
}

// ()( () | () ) () ((| ))

// () (() (  | ))  () (())