#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll n, k, l, r, delta, ans, L, R, res, p[100005], dp[100005], s[100005], sum[100005], ps[100005];
string str;
stack<int> stk;
void add(int pos) {
    if(str[pos] == '(') {
        if(p[pos] <= R) {
            if(str[p[pos] + 1] == '(' && p[p[pos] + 1] <= R) {
                sum[pos] = sum[p[pos] + 1] + 1;
                ps[pos] = ps[p[pos] + 1];
                ps[ps[pos]] = pos;
                ++sum[ps[pos]];
            }
            else sum[pos] = 1, ps[pos] = p[pos];
            ++sum[p[pos]];
            ps[p[pos]] = pos;
            res += sum[pos];
        }
    }
    if(str[pos] == ')') {
        if(p[pos] >= L) {
            if(str[p[pos] - 1] == ')' && p[p[pos] - 1] >= L) {
                sum[pos] = sum[p[pos] - 1] + 1;
                ps[pos] = ps[p[pos] - 1];
                ++sum[ps[pos]];
                ps[ps[pos]] = pos;
            }
            else sum[pos] = 1, ps[pos] = p[pos];
            ++sum[p[pos]];
            ps[p[pos]] = pos;
            res += sum[pos];
        }
    }
}
void del(int pos) {
    if(str[pos] == '(') {
        if(p[pos] <= R) {
            res -= sum[pos];
            if(str[p[pos] + 1] == '(' && p[p[pos] + 1] <= R) {
                --sum[ps[pos]];
                sum[p[pos] + 1] = sum[pos] - 1;
                sum[p[p[pos] + 1]] = 1;
                ps[p[p[pos] + 1]] = p[pos] + 1;
                ps[ps[pos]] = p[pos] + 1;
                ps[p[pos] + 1] = ps[pos];
                ps[pos] = 0;
            }
            else sum[pos] = 0, ps[pos] = 0;
            --sum[p[pos]];
            ps[p[pos]] = 0;
        }
        sum[pos] = 0;
    }
    if(str[pos] == ')') {
        if(p[pos] >= L) {
            res -= sum[pos];
            if(str[p[pos] - 1] == ')' && p[p[pos] - 1] >= L) {
                --sum[ps[pos]];
                sum[p[pos] - 1] = sum[pos] - 1;
                sum[p[p[pos] - 1]] = 1;
                ps[p[p[pos] - 1]] = p[pos] - 1;
                ps[ps[pos]] = p[pos] - 1;
                ps[p[pos] - 1] = ps[pos];
                ps[pos] = 0;
            }
            else sum[pos] = 0, ps[pos] = 0;
            --sum[p[pos]];
            ps[p[pos]] = 0;
        }
        sum[pos] = 0;
    }
}
ll calc(int l, int r) {
    while(L > l) add(--L);
    while(R < r) add(++R);
    while(L < l) del(L++);
    while(R > r) del(R--);
    return res;
}
void solve(int dl, int dr, int l, int r) {
    if(dl > dr || l > r) return;
    int mid = (dl + dr) >> 1, pos = l;
    ll mn = dp[l] + calc(l + 1, mid) + delta, tmp;
    for(int i = l; i <= r; ++i) {
        tmp = dp[i] + calc(i + 1, mid) + delta;
        if(tmp <= mn || (tmp == mn && s[i] > s[pos])) {
            pos = i, mn = tmp;
        }
    }
    if(mn < dp[mid] || (dp[mid] == mn && s[pos] + 1 > s[mid])) {
        dp[mid] = mn;
        s[mid] = s[pos] + 1;
    }
    solve(dl, mid - 1, l, pos);
    solve(mid + 1, dr, pos, r);
}
void CDQ(int l, int r) {
    if(l + 1 >= r) return;
    int mid = (l + r) >> 1;
    CDQ(l, mid);
    solve(mid, r - 1, l, mid - 1);
    CDQ(mid, r);
}
bool check() {
    fill(dp + 1, dp + 1 + n, 0x7f7f7f7f7f7f7f7f);
    dp[0] = 0;
    CDQ(0, n + 1);
    return s[n] >= k;
}
int main() {
    ios::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    cin >> n >> k >> str;
    str = '$' + str;
    for(int i = 1; i <= n; ++i) {
        if(str[i] == '(') p[i] = n + 1;
        else p[i] = 0;
    }
    for(int i = 1; i <= n; ++i) {
        if(str[i] == '(') stk.push(i);
        else if(!stk.empty()) {
            p[i] = stk.top();
            p[stk.top()] = i;
            stk.pop();
        }
    }
    L = 1, R = 0, res = 0;
    l = -10000000000ll, r = 10000000000ll;
    while(l <= r) delta = (l + r) >> 1, check()  (dp[n] - delta * k, delta + 1) : (delta - 1)
    cout << ans;
    cerr << '\n' << clock() << '\n';
    return 0;
}