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/* -----------------------
Autor: Tomasz Boguslawski
-------------------------- */
#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<fstream>
#include<iomanip>
#include<string>
#include<sstream>
#include<cstring>
#include<map>
#include<vector>
#include<set>
#include<queue>
#include<algorithm>
#include <fstream>
#include<math.h>

#define LL long long
#define FOR(x, b, e) for(LL x = b; x <= (e); x++)
#define FORS(x, b, e, s) for(LL x = b; x <= (e); x+=s)
#define FORD(x, b, e) for(LL x = b; x >= (e); x--)
#define VAR(v, n) __typeof(n) v = (n)
#define ALL(c) (c).begin(), (c).end()
#define FOREACH(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i)
#define DEBUG if (debug)
#define MIN(a,b) ((a>b)?b:a)
#define MAX(a,b) ((a>b)?a:b)

using namespace std;

char s[110000];

LL n,k;
LL N[110000]; // N[i] = nawiasowosc od indeksu i do jakiegos akurat wybranego i2
LL C[110000];

LL stac[110000];
LL stackCount;

void stackInit()
{
    stackCount=0;
}

inline void push(LL num)
{
    stackCount++; stac[stackCount]=num;
}

inline LL pop()
{
    LL res = stac[stackCount];
    stackCount--;
    return res;
}

void calculateN(LL i2)
{
    stackInit();
    FOR(i,1,i2+1) C[i]=0;
    LL total=0;
    LL dobreNaPrawo=0;
    LL j;
    FORD(i,i2,1)
    {
        if (s[i]==')')
        {
            push(i);
            //cout << "push: " << i << "\n";
        }
        else
        {
            if (stackCount>0)
            {
                j=pop();
                // mamy poprawne wyrazenie nawiasowe [i..j]
                dobreNaPrawo=C[j+1];
                C[i]=1+dobreNaPrawo;
                //cout << "poprawne: " << i << ".." << j << " C[" << i << "]=" << C[i] << "\n";
                total+=C[i];
            }
        }
        N[i]=total;
    }
}

void makeRandom()
{
    FOR(i,1,n) if (rand()%2==1) s[i]='('; else s[i]=')';
}

LL* X[101000]; // X[i][q] - podzial [1..i] na q przedzialow
const LL infi1=110000;
const LL infi=infi1*infi1;

LL calculateIt()
{
    FOR(i,0,n) X[i]=new LL[k+1];
    LL naw, nawMin;
    FOR(i,1,n)FOR(q,1,k) X[i][q]=infi;
    X[1][1]=0;
    FOR(i,2,n)
    {
        calculateN(i);
        X[i][1]=N[1]; // jeden przedzial
        //cout << "X[" << i << "][1]=" << X[i][1] << "\n";
        FOR(q,2,k)
        {
            //cout << " licze dla q=" << q << "\n";
            if (q>i) break; // nie liczymy podzialu na wiecej przedzialow niz znakow
            // liczymy X[i][q]
            // probujemy ostatni przedzial na wszystkie mozliwe sposoby
            nawMin=infi;
            // probujemy dzielic na q przedzialow:
            FORD(i1,i,q)
            {
                //cout << " probuje podzial na: 1.." << i1-1 << " " << i1 << ".." << i << " naw=" << N[i1]+X[i1-1][q-1] << "\n";
                naw=N[i1]+X[i1-1][q-1];
                if (naw<nawMin) nawMin=naw;
            }
            X[i][q]=nawMin;
            //cout << "X[" << i << "][" << q << "]=" << nawMin << "\n";
        }
    }
    return X[n][k];
}

/// MAIN
int main(int argc, char* argv[])
{
    // magic formula, which makes streams work faster:
	ios_base::sync_with_stdio(0);

	string s0;
	cin >> n; cin >> k;
	cin >> s0;
	FOR(i,1,n) s[i]=s0[i-1];

	if (n*k>60000000) cout << "0\n";
	else cout << calculateIt() << "\n";

	return 0;
}