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#pragma GCC optimize ("O3")
#include <bits/stdc++.h>
using namespace std;

#define FOR(i, b, e) for(int i = (b); i < (e); i++)
#define TRAV(x, v) for(auto &x: v)
#define PB push_back
#define SZ(x) ((int)x.size())
#define X first
#define Y second

using ll = long long;
using vi = vector<int>;
using ii = pair<int, int>;
constexpr int INF = 0x3f3f3f3f;

constexpr int N = 5324;

int naw[N][N];
int dp[N][N];

void solve() {
    int n, k;
    string s;
    cin >> n >> k >> s;
    FOR(i, 0, n) {
        int bal = 0;
        FOR(j, i, n) {
            bal += (s[j] == '(' ? 1 : -1);
            if(bal < 0) break;
            naw[i + 1][j + 1] = bal == 0;
        }
    }
    for(int i = n; i >= 1; i--) FOR(j, i, n + 1) naw[i][j] += naw[i + 1][j] + naw[i][j - 1] - naw[i + 1][j - 1];
    FOR(kk, 1, k + 1) dp[0][kk] = INF;
    FOR(i, 1, n + 1) dp[i][0] = INF;
    FOR(i, 1, n + 1) FOR(kk, 1, k + 1) {
        int akt = INF;
        FOR(j, 0, i) akt = min(akt, dp[j][kk - 1] + naw[j + 1][i]);
        dp[i][kk] = akt;
    }
    cout << dp[n][k] << '\n';
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    // int tt; cin >> tt;
    // FOR(te, 0, tt) {
    //     // cout << "Case #" << te + 1 << ": ";
    //     solve();
    // }
    solve();
    return 0;
}