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#include <bits/stdc++.h>

using namespace std;

#define ll long long

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)

typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;

typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;

typedef pair<int,int> ii;

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

const int MOD = 998244353;

ll read(){
    ll i;
    cin>>i;
    return i;
}

vi readvi(int n,int off=0,int shift=0){
    vi v(n+shift);
    rep(i,shift)v[i]=0;
    rep(i,n)v[i+shift]=read()+off;
    return v;
}

void YesNo(bool condition, bool do_exit=true) {
    if (condition)
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
    if (do_exit)
        exit(0);
}

int main(void ) {
    ios::sync_with_stdio(false);
    cin.tie(NULL);

    int n,k;
    cin >> n >> k;
    string s;
    cin >> s;

    vi pref_ends(n);

    vvi num_begins(n, vi(n,0));
    // num_begins[l][r] = num of begins at l which end at r.

    vvi begins_at_level(n);
    int balance=0;
    rep(i,n) {
        if (i>0) pref_ends[i] = pref_ends[i-1]; else pref_ends[i]=0;
        if (s[i] == ')') {
            begins_at_level[balance].resize(0);
            if (balance > 0) {
                --balance;
                for (auto b : begins_at_level[balance])
                    num_begins[b][i]++;
                pref_ends[i] += begins_at_level[balance].size();
            }
        }

        if (s[i] == '(') {
            begins_at_level[balance].push_back(i);
            ++balance;
        }
    }

    vvi pref_begins(n, vi(n,0));
    // pref_begins[l][r] = num of begins at l which end at <=r.

    rep(l,n)
        rep(r,n)
            pref_begins[l][r] = num_begins[l][r] + (r > 0 ? pref_begins[l][r-1] : 0);

    vvi pref_pref_begins(n, vi(n,0));
    // pref_pref_begins[l][r] = num of begins at <=l which end at <=r.

    rep(l,n)
        rep(r,n)
            pref_pref_begins[l][r] = pref_begins[l][r] + (l > 0 ? pref_pref_begins[l-1][r] : 0);

    vvi dp(n,vi(k,0));
    //dp[i][j] == suma nawiasowosci w s[:i] z j separatorami (j+1 częściami)

    rng(i,1,n) {
        dp[i][0] =  pref_ends[i];
        rng(j,1,min(i,k)) {
            dp[i][j] = INT_MAX;
            rep(t, i) {
                dp[i][j] = min(dp[i][j], dp[t][j - 1] + pref_ends[i] - pref_pref_begins[t][i]);
            }
        }
    }

    cout << dp[n-1][k-1] << endl;

    return 0;
}