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

#ifdef DEBUG
#include "debug.h"
#else
#define debug(...) ;
#endif

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

#define rep(i, n) for (int i = 0; i < (n); ++i)
#define repp(i, n, m) for (int i = (n); i < (m); ++i)

#define repr(i, n) for (int i = (n) - 1; i >= 0; --i)
#define reppr(i, n, m) for (int i = (m) - 1; i >= (n); --i)

using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using pi = pair<int, int>;
using pll = pair<ll, ll>;

template <typename T, typename V> void mini(T& a, V b) {if (b < a) a = b; }
template <typename T, typename V> void maxi(T& a, V b) {if (b > a) a = b; }

int n, k;
string s;

vll dp_before, dp_cur;
vector<vll> c;

void compute(int l, int r, int optl, int optr) {
    if (l > r)
        return;

    int mid = (l + r) >> 1;
    pair<ll, int> best = {ll(1e18), -1};

    for (int m = optl; m <= min(mid, optr); m++) {
        best = min(best, {(m ? dp_before[m - 1] : 0) + c[m][mid], m});
    }

    dp_cur[mid] = best.first;
    int opt = best.second;

    compute(l, mid - 1, optl, opt);
    compute(mid + 1, r, opt, optr);
}

void solve() {
    cin >> n >> k >> s;

    c.resize(n, vll(n));

    rep(i, n) {
        int lv = 0, cnt = 0;

        for (int j = i; j < n; ++j) {
            lv += s[j] == '(' ? 1 : -1;
            cnt += lv == 0;

            if (lv < 0)
                lv = -10;

            c[i][j] = cnt;
        }
    }

    debug(c);

    rep(i, n) {
        for (int j = i-1; j >= 0; --j)
            c[j][i] += c[j+1][i];
    }

    debug(c);

    dp_before.resize(n);
    dp_cur.resize(n);

    for (int i = 0; i < n; i++)
        dp_before[i] = c[0][i];

    for (int i = 1; i < k; i++) {
        compute(0, n - 1, 0, n - 1);
        dp_before = dp_cur;
    }

    debug(dp_before);

    cout << dp_before.back() << '\n';
}

int main() {
#ifndef DEBUG
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
#endif
    int z = 1;
    // scanf("%d", &z);
    while (z--)
        solve();
    return 0;
}