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// Karol Kosinski 2022
#include <bits/stdc++.h>
#define FOR(i,a,b) for(int i=(a),_b=(b);i<_b;++i)
#define FR_(i,a,b) for(int i=(a),_b=(b);i<=_b;++i)
#define FD_(i,b,a) for(int i=(b),_a=(a);i>=_a;--i)
#define ALL(c) (c).begin(),(c).end()
#define SIZE(c) int((c).size())
#define TIE(x...) int x;tie(x)
#define X first
#define Y second
#ifndef ENABLE_DEBUG
#define DEB(k,p,f,x...)
#else
#define DEB(k,p,f,x...) {if(k)printf("--------%4d : %s\n",__LINE__,__FUNCTION__);if(p)f(x);}
#endif
#define DEBL DEB(1,1,void,0)
#define DEBF(f,x...) DEB(1,1,f,x)
#define DEBC(p,x...) DEB(0,p,printf,x)
#define DEBUG(x...) DEB(0,1,printf,x)
using namespace std;
using LL = long long;
using ULL = unsigned long long;
using PII = pair<int, int>;
using TIII = tuple<int, int, int>;

constexpr int NX = 100'005;

char A[NX];
vector<int> Nodes, S;

namespace BellmanFord
{
    // static constexpr int INFTY = 1e9 + 1;

    int n, D[NX];
    vector<PII> G[NX];

    void add(int u, int v, int w)
    {
        G[u].emplace_back(v, w);
        DEBUG("** ( %d, %d ) [ %d ]\n", u, v, w);
    }
    void clear() { FOR(i,0,n) G[i].clear(); }

    void printD()
    {
        FOR(i,0,n) DEBUG("D[%d] = %d\n", i, D[i]);
        DEBUG("----------\n")
    }

    void init(int ng, int k)
    {
        n = ng;
        D[0] = 0;
        FOR(i,1,n) D[i] = G[0][ i - 1 ].Y;
        DEBF(printD);
        FOR(st,1,k)
        {
            FD_( u, n - 1, st)
            {
                for ( auto& ed : G[u] ) if ( D[ed.X] > D[u] + ed.Y )
                    D[ed.X] = D[u] + ed.Y;
            }
            DEBF(printD);
        }
    }
}

void find_nodes(int n)
{
    Nodes.push_back(1);
    FR_(i,2,n)
    {
        if ( A[ i - 1 ] == '(' and A[i] == ')' )
            Nodes.push_back(i);
    }
    // if ( Nodes.back() != n )
        // Nodes.push_back( n + 1 );
}

int compute(int start, int n)
{
    int result = 0, ind =  start + 1;
    S.clear();
    S.push_back( 0 );
    FR_( i, Nodes[start], n )
    {
        if ( A[i] == '(' )
        {
            S.push_back( 0 );
        }
        else
        {
            S.pop_back();
            if ( S.empty() )
            {
                S.push_back( 0 );
            }
            else
            {
                if ( Nodes[ind] == i )
                {
                    BellmanFord::add( start, ind, result );
                    ++ ind;
                }
                result += ( ++ S.back() );
            }
        }
    }
    BellmanFord::add( start, ind, result );
    return result;
}

int main()
{
    int n, k; scanf("%d%d%s", &n, &k, A + 1);
    find_nodes(n);
    DEBUG("#Nodes : %d\n", SIZE(Nodes) );
    if ( n == k or SIZE(Nodes) <= k )
    {
        printf("0\n");
        return 0;
    }
    if ( k == 1 )
    {
        printf( "%d\n", compute(0, n) );
        return 0;
    }
    FOR( i, 0, SIZE(Nodes) )
    {
        compute( i, n );
    }
    BellmanFord::init( SIZE(Nodes) + 1, k );
    printf("%d\n", BellmanFord::D[ SIZE(Nodes) ] );
    return 0;
}