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#include <bits/stdc++.h>
using namespace std;
#define endl "\n"
#define mp make_pair
#define st first
#define nd second
#define pii pair<int, int>
#define vi vector<int>
#define pb push_back
#define _upgrade ios_base::sync_with_stdio(0), cout.setf(ios::fixed), cout.precision(10), cin.tie(0), cout.tie(0);
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define fwd(i, a, b) for (int i = (a); i < (b); ++i)
#define trav(a, x) for (auto &a : x)
#define all(c) (c).begin(), (c).end()
#define sz(X) (int)((X).size())
typedef long double ld;
typedef unsigned long long ull;
typedef long long ll;
#ifdef LOCAL
ostream &operator<<(ostream &out, string str) {
   for (char c : str)
      out << c;
   return out;
}
template <class L, class R> ostream &operator<<(ostream &out, pair<L, R> p) { return out << "(" << p.st << ", " << p.nd << ")"; }
template <class L, class R, class S> ostream &operator<<(ostream &out, tuple<L, R, S> p) {
   auto &[a, b, c] = p;
   return out << "(" << a << ", " << b << ", " << c << ")";
}
template <class T> auto operator<<(ostream &out, T a) -> decltype(a.begin(), out) {
   out << '{';
   for (auto it = a.begin(); it != a.end(); it = next(it))
      out << (it != a.begin() ? ", " : "") << *it;
   return out << '}';
}
void dump() { cerr << "\n"; }
template <class T, class... Ts> void dump(T a, Ts... x) {
   cerr << a << ", ";
   dump(x...);
}
#define debug(...) cerr << "[" #__VA_ARGS__ "]: ", dump(__VA_ARGS__)
#else
#define debug(...) 42
#endif

#define int long long
namespace BRUT1 {
   const int MAXN = 5000;
   const int inf = 1e18;

   int sm[MAXN][MAXN];
   int naw[MAXN][MAXN];

   int dp[MAXN][MAXN];

   int solve(string s, int limit) {

      rep(i, MAXN) rep(j, MAXN) dp[i][j] = inf;
      dp[0][0] = 0;

      int n = sz(s);
      for (int l = 1; l < MAXN; l++)
         rep(i, sz(s)) {
            int j = l + i;
            if (j > n)
               continue;
            sm[i][j] = sm[i][j - 1] + (s[j - 1] == ')' ? -1 : +1);
            if (sm[i][j] < 0)
               sm[i][j] = -inf;
            naw[i][j] = naw[i][j - 1] + naw[i + 1][j] - naw[i + 1][j - 1] + (sm[i][j] == 0);
            debug(i, j, naw[i][j], sm[i][j]);
         }

      rep(i, n + 1) for (int k = 1; k <= limit; k++) rep(j, i) dp[i][k] = min(dp[i][k], dp[j][k - 1] + naw[j][i]);
      return dp[n][limit];
   }

} // namespace BRUT1
int32_t main() {
   _upgrade;
   int n, k;
   cin >> n >> k;
   string s;
   cin >> s;
   int res = BRUT1::solve(s, k);
   cout << res << endl;
}