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#include <bits/stdc++.h>
using namespace std;
int n, k;

long long mw(int s, vector<vector<long long>> &dp, int d, vector<vector<long long>> &chs)
{
    if (chs[s][d] != -1)
        return chs[s][d];
    if (s >= n)
        return 1e18;
    if (d == k)
        return dp[s][n - 1];
    long long lmao = 1e18;
    for (int i = s; i < n; i++)
        lmao = min(lmao, dp[s][i] + mw(i + 1, dp, d + 1, chs));
    chs[s][d] = lmao;
    return lmao;
}

int main()
{
    ios_base::sync_with_stdio(0);
    string s;
    cin >> n >> k >> s;
    vector<vector<bool>> w(n, vector<bool>(n));
    vector<vector<long long>> dp(n, vector<long long>(n));
    vector<vector<long long>> csh(n + 1, vector<long long>(n + 1, -1));
    for (int i = 0; i < n; i++)
    {
        int c = 0;
        for (int j = i; j < n; j++)
        {
            if (s[j] == ')')
                c--;
            else
                c++;
            if (c < 0)
                break;
            if (c == 0)
                w[i][j] = 1;
        }
    }
    for (int l = 1; l <= n; l++)
    {
        for (int i = 0; i + l <= n; i++)
        {
            dp[i][i + l - 1] = w[i][i + l - 1];
            if (l > 1)
                dp[i][i + l - 1] += dp[i + 1][i + l - 1] + dp[i][i + l - 2];
            if (l > 2)
                dp[i][i + l - 1] -= dp[i + 1][i + l - 2];
            // cout << i << ' ' << l << ' ' << dp[i][i + l - 1] << '\n';
        }
    }
    // vector<vector<long long>> dp2(n, vector<long long>(n));

    cout << mw(0, dp, 1, csh) << '\n';
}