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

typedef long long LL;
typedef long double LD;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;

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

template<typename _T> inline void _DBG(const char *s, _T x) { cerr << s << " = " << x << "\n"; }
template<typename _T, typename... args> void _DBG(const char *s, _T x, args... a) { while(*s != ',') cerr << *s++; cerr << " = " << x << ','; _DBG(s + 1, a...); }

#ifdef LOCAL
#define _upgrade ios_base::sync_with_stdio(0);
#define DBG(...) _DBG(#__VA_ARGS__, __VA_ARGS__)
#else
#define _upgrade ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define DBG(...) (__VA_ARGS__)
#define cerr if(0) cout
#endif

// ********************** CODE ********************** //

const int N = 4005;
const int INF = (LL) 1e9 + 7;

int cnt[N][N];

int n, k;
char s[N];

int dp[N][N];
int opt[N][N];

int val(int i, int j)
{
    return cnt[i][j];
}

void calc(int i, int l, int r, int optL, int optR)
{
    if (l > r)
        return;
    int m = (l + r) / 2;

    opt[i][m] = optL;
    for(int j = optL; j <= min(m - 1, optR); j++)
    {
        if(dp[i][m] > dp[i - 1][j] + val(j + 1, m))
        {
            dp[i][m] = dp[i - 1][j] + val(j + 1, m);
            opt[i][m] = j;
        }
    }
    calc(i, l, m - 1, optL, opt[i][m]);
    calc(i, m + 1, r, opt[i][m], optR);
}

int main()
{
    _upgrade
    
    cin >> n >> k >> (s + 1);
    for (int i = 1; i <= n; i++)
    {
        int bal = 0;
        for (int j = i; j <= n; j++)
        {
            if (s[j] == '(')
                bal++;
            else
                bal--;
            if (bal < 0)
                break;
            if (bal == 0)
                cnt[i][j] = 1;
        }
    }

    for (int d = 2; d <= n; d++)
    {
        for (int i = 1, j = d; j <= n; i++, j++)
        {
            cnt[i][j] += cnt[i + 1][j] + cnt[i][j - 1] - cnt[i + 1][j - 1];
        }
    }

    for (int i = 0; i <= k; i++)
        for (int j = 0; j <= n; j++)
            dp[i][j] = INF;

    dp[0][0] = 0;

    for (int i = 1; i <= k; i++)
    {
        calc(i, 1, n, 0, n);
    }

    cout << dp[k][n] << "\n";

    return 0;
}