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#include <bits/stdc++.h>
 
using namespace std;
 
//#define endl '\n'
#define L long long
#define MP make_pair
#define REP(i, n) for(int i = 0; i < n; ++i)
#define REPR(i, n) for(int i = n - 1; i >= 0; --i)
#define FOR(i, a, b) for(int i = a; i < b; ++i)
#define FORR(i, a, b) for(int i = b - 1; i >= a; --i)
#define EB emplace_back
#define ST first
#define ND second
#define S size
#define RS resize
 
template<class T> using P = pair<T, T>;
template<class T> using V = vector<T>;
 
int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    int inf = 1e9;
    int n, k;
    cin >> n >> k;
    V<int> a(n);
    REP(i, n) {
        char c;
        cin >> c;
        a[i] = c == '(' ? 1 : -1;
    }

    
    V<V<bool>> b(n, V<bool>(n));
    REP(i, n) {
        int sum = 0;
        FOR(j, i, n) {
            sum += a[j];
            if (sum < 0) break;
            if (sum == 0) b[i][j] = true;
        }
    }

    V<V<int>> w(n, V<int>(n));
    REP(i, n - 1) {
        w[i][i + 1] = b[i][i + 1];
    }
    FOR(d, 2, n) {
        REP(l, n - d) {
            int r = l + d;
            w[l][r] = b[l][r] + w[l][r - 1] + w[l + 1][r] - w[l + 1][r - 1];
        }
    }

    V<V<int>> dp(n, V<int>(k, inf));
    REP(i, n) {
        dp[i][0] = w[0][i];
        if (i == 0) continue;
        FOR(j, 1, k) {
            int m = dp[i - 1][j - 1];
            REP(l, i - 1) {
                m = min(m, dp[l][j - 1] + w[l + 1][i]);
            }
            dp[i][j] = m;
        }
    }
    cout << dp[n - 1][k - 1] << '\n';
}

// g++ -std=c++17 -Wall -Wextra -Wshadow -Wconversion -D_GLIBCXX_DEBUG -O3 naw.cpp -o a