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#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ssize(x) int(x.size())
#define pb push_back
#define mp make_pair
#define all(a) begin(a),end(a)
// #define FOR(i, l, r) for(int i = (l); i <= (r); ++i)
#define FOR(i, l, r) for(int i = (l); i < (r); ++i)
#define FORE(i, l, r) for(int i = (l); i <= (r); ++i)
// # define REP(i, n) FOR(i, 0, (n) - 1)
# define REP(i, n) FORE(i, 0, (n) - 1)
#define FORR(x,arr) for(auto &x: arr)
#define REE(s_) {cout<<s_<<'\n';exit(0);}
#define GET(arr) for(auto &i: (arr)) sc(i)
#define e1 first
#define e2 second
#define INF 0x7f7f7f7f
#define debug(x...) cerr << "[" #x "]: ", [](auto... $) {((cerr << $ << "; "),...); }(x), cerr << '\n'
typedef std::pair<int,int> pi;
typedef std::vector<int> vi;
typedef std::vector<std::string> vs;
typedef int64_t ll;
typedef uint64_t ull;
using namespace std;
using namespace __gnu_pbds;

#ifdef ONLINE_JUDGE
#define debug(...) {}
#endif
#ifdef _WIN32
#define getchar_unlocked() _getchar_nolock()
#define _CRT_DISABLE_PERFCRIT_LOCKS
#endif
template<class A, class B> auto& operator<<(ostream &o, pair<A, B> p) { return o << '(' << p.first << ", " << p.second << ')'; }
template<class T> auto operator<<(ostream &o, T x) -> decltype(x.end(), o) { o << '{'; int i = 0; for(auto e : x) o << (", ")+2*!i++ << e; return o << '}'; }
inline int fstoi(const string &str){auto it=str.begin();bool neg=0;int num=0;if(*it=='-')neg=1;else num=*it-'0';++it;while(it<str.end()) num=num*10+(*it++-'0');if(neg)num*=-1;return num;}
inline void getch(char &x){while(x = getchar_unlocked(), x < 33){;}}
inline void getstr(string &str){str.clear(); char cur;while(cur=getchar_unlocked(),cur<33){;}while(cur>32){str+=cur;cur=getchar_unlocked();}}
template<typename T> inline bool sc(T &num){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){if(c == EOF) return false;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; return true;}template<typename T, typename ...Args> inline void sc(T &num, Args &...args){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; sc(args...); }
template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; //s.find_by_order(), s.order_of_key() <- works like lower_bound
template<typename T> using ordered_map = tree<T, int, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
// 1 << 19 if segtree where merges matter.
#define N 1000001

vector<vector<ll>> ile;
vector<long long> dp_before, dp_cur;
void compute(int l, int r, int optl, int optr) {
    if (l > r)
        return;

    int mid = (l + r) >> 1;
    pair<long long, int> best = {LLONG_MAX, -1};

    for (int k = optl; k <= min(mid, optr); k++) {
        best = min(best, {(k ? dp_before[k - 1] : 0) + ile[k][mid], k});
    }

    dp_cur[mid] = best.first;
    int opt = best.second;

    compute(l, mid - 1, optl, opt);
    compute(mid + 1, r, opt, optr);
}


int main(){
    ios_base::sync_with_stdio(0);cin.tie(0);
    int n, k;
    sc(n,k);
    string s;
    getstr(s);
    /* ll ile[n][n]; */
    /* vector<vector<ll>> ile(n, vector<ll>(n, 0)); */
    ile = vector<vector<ll>>(n, vector<ll>(n, 0));
    REP(i,n)
        ile[i][i] = 0;
    int balpre[n];
    balpre[0] = s[0] == '(' ? 1 : -1;
    FOR(i,1,n){
        /* balpre[i] = balpre[i - 1] + (s[0] == '(' ? 1 : -1); */
        balpre[i] = balpre[i - 1] + (s[i] == '(' ? 1 : -1);
    }
    for(int l = n - 2; l >= 0; --l){
        /* int mnbalpre = INF; */
        int mnbalpre = balpre[l];
        for(int r = l + 1; r < n; ++r){
            mnbalpre = min(mnbalpre, balpre[r]);
            // AMPPZ I zadans 1:1
            /* ile[l][r] = ile[l + 1][r] + ile[l][r - 1] - ile[l][r] + ((l ? balpre[l - 1] : 0) == balpre[r] && mnbalpre == balpre[r]); */
            /* ile[l][r] = ile[l + 1][r] + ile[l][r - 1] - ile[l + 1][r - 1] + ((l ? balpre[l - 1] : 0) == balpre[r] && mnbalpre == balpre[r]); */
            ile[l][r] = ile[l + 1][r] + ile[l][r - 1] - (l + 1 <= r - 1 ? ile[l + 1][r - 1] : 0) + ((l ? balpre[l - 1] : 0) == balpre[r] && mnbalpre == balpre[r]);
        }
    }

    /* debug(ile); */
    dp_before.resize(n); dp_cur.resize(n);
    for (int i = 0; i < n; i++)
        dp_before[i] = ile[0][i];

    for (int i = 1; i < k; i++) {
        compute(0, n - 1, 0, n - 1);
        dp_before = dp_cur;
    }
    /* vector<vector<ll>> dp(k + 2, vector<ll>(n + 1)); // don't need nk mem */
    /* dp[0][0] = 0; */
    /* FOR(i,0,n){ */
    /*     dp[0][i + 1] = ile[0][i]; */
    /* } */
    /* FORE(crk, 1, k + 1){ */
    /*     dp[crk][0] = 0; */
    /*     auto rec = [&](auto &self, int l, int r, int optl, int optr) -> void{ */
    /*         if(l > r) */
    /*             return; */
    /*         int crpos = (l + r) / 2; */
    /*         pair<int,int> best{INF, -1}; // XXX LONG_LONG_MAX if ll */
    /*         FORE(i, min(optl, crpos), min(optr, crpos)){ */
    /*             int cr = dp[crk - 1][i] + ile[i][crpos]; // tutaj dp exclusive */
    /*             best = min(best, {cr, i}); */
    /*         } */
    /*         dp[crk][crpos + 1] = best.first; */
    /*         self(self, l, crpos - 1, optl, best.second); */
    /*         self(self, crpos + 1, r, best.second, optr); */
    /*     }; */
    /*     rec(rec, 0, n - 1, 0, n); */
    /* } */
    /* /1* debug(dp); *1/ */
    /* /1* // n - 1 vs n? *1/ */
    /* cout << dp[k + 1][n - 1] << '\n'; */
    cout << dp_before[n - 1] << '\n';
}