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#include <iostream>
#include <climits>

using namespace std;

const int MAX_N = 307;

int n, K;
int a[MAX_N];
int pass[MAX_N][MAX_N];
int dp[MAX_N][MAX_N];

void init() {
    cin >> n >> K;

    for (int i = 1; i <= n; i++) {
        char c;
        cin >> c;

        if (c == '(')
            a[i] = 1;
        else
            a[i] = -1;
    }
}

void preprocess() {
    for (int i = 1; i <= n; i++) {
        if (a[i] == -1) {
            continue;
        }

        int pref = 1;

        for (int j = i + 1; j <= n; j++) {
            pref += a[j];

            if (pref < 0) {
                break;
            }

            if (pref == 0) {
                for (int l = 1; l <= i; l++) {
                    for (int r = j; r <= n; r++) {
                        pass[l][r]++;
                    }
                }
            }
        }
    }
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    init();
    preprocess();

    for (int k = 1; k <= K; k++) {
        for (int i = 1; i <= n; i++) {
            dp[k][i] = MAX_N * MAX_N;
        }
    }

    for (int i = 1; i <= n; i++) {
        dp[1][i] = pass[1][i];
    }

    for (int k = 2; k <= K; k++) {
        for (int i = 1; i <= n; i++) {
            int mini = MAX_N * MAX_N;

            for (int j = 1; j < i; j++) {
                mini = min(dp[k - 1][j] + pass[j + 1][i], mini);
            }

            dp[k][i] = mini;
        }
    }

    /*
    cout << "PASS:\n";
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            cout << pass[i][j] << ' ';
        }
        cout << '\n';
    }
    cout << '\n';
    cout << "DP:\n";
    for (int k = 0; k < K; k++) {
        for (int i = 0; i <= n; i++) {
            cout << dp[k][i] << ' ';
        }

        cout << '\n';
    }
    */

    cout << dp[K][n] << '\n';

    return 0;
}