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

#define sim template <class c
#define ris return *this
#define dor > debug &operator<<
#define eni(x)                                                                    \
    sim > typename enable_if<sizeof dud<c>(0) x 1, debug &>::type operator<<(c i) \
    {
sim > struct rge
{
    c b, e;
};
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c *x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug
{
#ifdef XOX
    ~debug()
    {
        cerr << endl;
    }
    eni(!=) cerr << boolalpha << i;
    ris;
} eni(==) ris << range(begin(i), end(i));
}
sim, class b dor(pair<b, c> d)
{
    ris << "" << d.first << " --> " << d.second << "";
}
sim dor(rge<c> d)
{
    *this << "[";
    for (auto it = d.b; it != d.e; ++it)
        *this << ", " + 2 * (it == d.b) << *it;
    ris << "]";
}
#else
    sim dor(const c &)
    {
        ris;
    }
#endif
}
;

#define imie(...) "" << #__VA_ARGS__ " = " << (__VA_ARGS__) << ", "
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define f first
#define s second

#define sz(x) (x).size()
#define all(x) (x).begin(), (x).end()
#define vt vector

using ll = long long;
using pi = pair<int, int>;
using pll = pair<ll, ll>;

using vi = vt<int>;
using vvi = vt<vi>;
using vll = vt<ll>;
using vvll = vt<vll>;
using vs = vt<string>;
using vpi = vt<pi>;
using vvpi = vt<vpi>;
using vpll = vt<pll>;
using vvpll = vt<vpll>;

const int mod = 1e9 + 7;
const int nax = 3e2 + 9;
int n, k;
string str;
int dp[nax][nax];
int ile[nax][nax];
int good(string str)
{
    int sum = 0;
    for (char c : str)
    {
        if (c == '(')
            sum++;
        else
            sum--;
        if (sum < 0)
            return 0;
    }
    if (sum == 0)
        return 1;
    return 0;
}
int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie();
    cin >> n >> k;
    cin >> str;
    for (int i = 0; i < n - 1; i++)
    {
        if (str[i] == '(' && str[i + 1] == ')')
            ile[i][i + 1] = 1;
    }
    for (int add = 2; add < n; add++)
    {
        for (int l = 0; l + add < n; l++)
        {
            int r = l + add;
            ile[l][r] += ile[l][r - 1];
            ile[l][r] += ile[l + 1][r];
            ile[l][r] -= ile[l + 1][r - 1];
            if (good(str.substr(l, add + 1)))
                ile[l][r]++;
        }
    }
    for (int i = 0; i <= n; i++)
    {
        for (int j = 0; j <= k; j++)
        {
            dp[i][j] = 1e9;
        }
    }
    dp[0][0] = 0;
    // dp[i][k] = minimalny koszt, zeby podzielic przedzial [0,i-1] na k segmentow
    for (int i = 1; i <= n; i++)
    {
        for (int seg = 1; seg <= i; seg++)
        {
            for (int j = 0; j < i; j++)
            {
                dp[i][seg] = min(dp[i][seg], dp[j][seg - 1] + ile[j][i - 1]);
            }
        }
    }
    cout << dp[n][k];
}