/**
Zubayet Zaman Zico

codeforces : I_See_You
hackerrank : I_See_You
codechef   : xico
spoj       : xico
email      : hhoho07@gmail.com
**/

//#include <stdio.h>
//#include <iostream>
//#include <cstring>
//#include <cmath>
//#include <algorithm>
//#include <string>
//#include <vector>
//#include <map>
//#include <set>
//#include <queue>
//#include <cstdlib>
//#include <limits>
//#include <iostream>
//#include <sstream>
//#include <unordered_set>
//#include <unordered_map>
//#include <random>
#include <bits/stdc++.h>
//#include <ext/pb_ds/assoc_container.hpp>
//using namespace __gnu_pbds;
using namespace std;


//#define gc getchar unlocked
//#ifndef ONLINE JUDGE
#define gc getchar
//#endif // ONLINE JUDGE

//#define pc putchar_unlocked
//#ifndef ONLINE JUDGE
#define pc putchar
//#endif // ONLINE JUDGE

#define fRead           freopen("input.txt","r",stdin)
#define fWrite          freopen("output.txt","w",stdout)

#define eps             1e-9
#define inf             0x3f3f3f3f
#define INF             2e18
#define LL              long long
#define ULL             unsigned long long
#define PI              acos(-1.0)
#define pb              push_back
#define mk              make_pair
#define pii             pair<int,int>
#define pLL             pair<LL,LL>
#define ff              first
#define ss              second
#define all(a)          a.begin(),a.end()
#define rall(a)         a.rbegin(),a.rend()
#define SQR(a)          ((a)*(a))
#define Unique(a)       sort(all(a)),a.erase(unique(all(a)),a.end())
#define min3(a,b,c)     min(a,min(b,c))
#define max3(a,b,c)     max(a,max(b,c))
#define min4(a,b,c,d)   min(min(a,b),min(c,d))
#define max4(a,b,c,d)   max(max(a,b),max(c,d))
#define max5(a,b,c,d,e) max(max3(a,b,c),max(d,e))
#define min5(a,b,c,d,e) min(min3(a,b,c),min(d,e))
#define Iterator(a)     __typeof__(a.begin())
#define rIterator(a)    __typeof__(a.rbegin())
#define FOR(a,it)       for(Iterator(a) it = a.begin();it != a.end(); it++)
#define rFOR(a,it)      for(rIterator(a) it = a.rbegin();it != a.rend(); it++)
#define FastRead        ios_base::sync_with_stdio(0);cin.tie(0)
#define CasePrint       pc('C'); pc('a'); pc('s'); pc('e'); pc(' '); write(qq++,false); pc(':'); pc(' ')
#define vi              vector <int>
#define vL              vector <LL>
#define For(I,A,B)      for(int I = (A); I  < (B); ++I)
#define rFor(I,A,B)     for(int I = (A); I >= (B); --I)
#define Rep(I,N)        For(I,0,N)
#define REP(I,N)        For(I, 1, N + 1)
#define gti             int, vi, greater<int>
#define gtL             LL, vL, greater<LL>
#define Found(a, b)     a.find(b) != a.end()
#define y0              y00

const int MOD = 1e9 + 7;
int fx[] = {-1,+0,+1,+0,+1,+1,-1,-1,+0};
int fy[] = {+0,-1,+0,+1,+1,-1,+1,-1,+0};
int day[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
//template <typename T> using orderset = tree <T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>; // find_by_order, order_of_key
template <typename T> inline bool isLeap(T y) {return (y % 400 == 0) || (y % 100 ? y % 4 == 0 : false); }
template <typename T> inline T GCD (T a,T b ) {a = abs(a);b = abs(b); if(a < b) swap(a, b); while ( b ) { a = a % b; swap ( a, b ); } return a;}
template <typename T> inline T EGCD(T a,T b,T &x,T &y){if(a == 0) {x = 0;y = 1;return b;}T x1, y1;T d = EGCD(b % a, a, x1, y1);x = y1 - (b / a) * x1;y = x1;return d;}
template <typename T> inline T LCM(T x,T y){T tp = GCD(x,y);if( (x / tp) * 1. * y > 9e18) return 9e18;return (x / tp) * y;}
template <typename T> inline T BigMod(T A,T B,T M = MOD){A %= M;T ret = 1;while(B){if(B & 1) ret = (ret * A) % M;A = (A * A) % M;B = B >> 1;}return ret;}
template <typename T> inline T InvMod (T A,T M = MOD){return BigMod(A,M-2,M);}
template <typename T> void Compress(T * in, int n, int f = 0){vector <T> vv;for(int i = f; i < n + f; i++) vv.pb(in[i]);Unique(vv);for(int i = f; i < n + f; i++) in[i] = lower_bound(all(vv), in[i]) - vv.begin();}
//template <typename T> void Compress(vector <T> &in){vector <T> vv;for(T x : in) vv.pb(x);Unique(vv);for(int i = 0; i < in.size(); i++) in[i] = lower_bound(all(vv), in[i]) - vv.begin();}
/*---------------------------fast I/O------------------------------------*/
#define scani2(a,b) scani(a) , scani(b)
#define scani3(a,b,c) scani(a), scani(b), scani(c)
#define scani4(a,b,c,d) scani(a), scani(b), scani(c), scani(d)
#define scani5(a,b,c,d,e) scani(a), scani(b), scani(c), scani(d) , scani(e)
template <typename T> T scani(T &n){n = 0;bool negative = false;char c = gc();while( c < '0' || c > '9'){if(c == '-') negative = true;c = gc();}while(c >= '0' && c <= '9'){n = n*10 + c-48;c = gc();}if(negative) n = ~(n-1);return n;}
template <typename T> void write(T n,int type = true){if(n<0) {pc('-');n = -n;}if(!n) {pc('0');if(type==32) pc(' '); else if(type) pc('\n'); return;}char buff[22];int len = 0;while(n) buff[len++] = n%10+48,n/=10;for(int i=len-1;i>=0;i--) pc(buff[i]);if(type==32) pc(' '); else if(type) pc('\n');}
int scans(char *a){int i=0;char c = 0;while(c < 33) c = gc();while(c > 33){a[i++] = c;c = gc();}a[i] = 0;return i;}
/*********************************************** End of template *********************************************/


#ifdef Sieve
const int pSz = 2000006;
bool np[pSz + 10]; vi prime; int prime_size;void sieve(){np[0] = np[1] = 1;prime.pb(2);for(LL i = 4; i <= pSz; i+=2) np[i] = 1;for(LL i = 3; i <= pSz; i+=2){if(!np[i]){prime.pb(i);for(LL j = i * i; j <= pSz; j += (i << 1)) np[j] = 1;}}prime_size = prime.size();}
#endif

#ifdef Combi
const int nSz = 2000006;
LL F[nSz + 1], tMod = MOD;
void Factorial(){ F[0] = 1; for(int i = 1; i <= nSz; i++) F[i] = (F[i - 1] * i) % tMod; }
inline LL nCr(int n, int r) { if(n < r) return 0; return (F[n] * InvMod((F[n - r] * F[r]) % tMod, tMod)) % tMod; }

#endif

#ifdef Z_Algo
void zAlgo(char *s, int *z){
    int L, R, sz; sz = strlen(s); z[0] = L = R = 0;
    For(i, 1, sz) { z[i] = 0; if(i <= R) z[i] = min(z[i - L], R - i + 1); while(i + z[i] < sz && s[i + z[i]] == s[z[i]]) z[i]++; if(i + z[i] - 1 > R) L = i, R = i + z[i] - 1; }
}void zAlgo(string &s, int *z){
    int L, R, sz; sz = s.size(); z[0] = L = R = 0;
    For(i, 1, sz) { z[i] = 0; if(i <= R) z[i] = min(z[i - L], R - i + 1); while(i + z[i] < sz && s[i + z[i]] == s[z[i]]) z[i]++; if(i + z[i] - 1 > R) L = i, R = i + z[i] - 1; }
}void zAlgo(int *s, int *z, int n){
    int L, R, sz; sz = n; z[0] = L = R = 0;
    For(i, 1, sz) { z[i] = 0; if(i <= R) z[i] = min(z[i - L], R - i + 1); while(i + z[i] < sz && s[i + z[i]] == s[z[i]]) z[i]++; if(i + z[i] - 1 > R) L = i, R = i + z[i] - 1; }
}
#endif // Z_Algo


/********************************************* define Template *************************************************/

template <typename T> inline T SqrDis(T x1, T y1, T x2, T y2){return SQR(x1 - x2) + SQR(y1 - y2);}
template <typename T> inline T Area2(T Ax, T Ay, T Bx, T By, T Cx, T Cy){T ret = Ax * (By - Cy) + Bx * (Cy - Ay) + Cx * (Ay - By);
    if(ret < 0) return ret = -ret;
    return ret;
}
/**************************************************** GEO ******************************************************/
const int N = 2000006; /** need to update this **/
const int M = 2097152 + 10;
const ULL hs = 3797;
/** use data types carefully try to take 'long long' **/
const int base = 555;

set <int> close;
int Tree[N << 2], Pr[N << 2], cum[N];
int n, qr;
char ch[N];

void push_down(int node, int b, int e){
    if(Pr[node] == 0 || b == e) return ;
    int mid = b + e >> 1;
    int lf = node << 1;
    int rt = lf | 1;

    Pr[lf] += Pr[node];
    Pr[rt] += Pr[node];
    Tree[lf] += Pr[node];
    Tree[rt] += Pr[node];

    Pr[node] = 0;
}

void built(int node, int b, int e) {
    if(b == e) {
        Tree[node] = cum[b];
        return ;
    }
    int mid = b + e >> 1;
    int lf = node << 1;
    int rt = lf | 1;
    built(lf, b, mid);
    built(rt, mid + 1, e);
    Tree[node] = min(Tree[lf], Tree[rt]);
}

void update(int node, int b, int e, int i, int j, int v) {
    push_down(node, b, e);
    if(b > j || e < i) return ;
    if(b >= i && e <= j){
        Tree[node] += v;
        Pr[node] += v;
        return ;
    }
    int mid = b + e >> 1;
    int lf = node << 1;
    int rt = lf | 1;
    update(lf, b, mid, i, j, v);
    update(rt, mid + 1, e, i, j, v);
    Tree[node] = min(Tree[lf], Tree[rt]);
}

int query(int node, int b, int e){
    push_down(node, b, e);
    if(b == e) return b;
    int mid = b + e >> 1;
    int lf = node << 1;
    int rt = lf | 1;
//    cout << node << ' ' << b << ' ' << e << ' ' << Tree[lf] << ' ' << Tree[rt] << '\n';
    if(Tree[rt] >= 2) return query(lf, b, mid);
    return query(rt, mid + 1, e);
}

int res[N];

int main()
{
    scanf("%d %d", &n, &qr);
    scanf("%s", ch + 1);
    For(i, 1, n + 1) {
        cum[i] += cum[i - 1];
        if(ch[i] == '(') {
            cum[i]++;
        }
        else {
            cum[i]--;
            close.insert(i);
        }
    }

    built(1, 1, n);
    Rep(i, qr) {
        int x; scanf("%d", &x);
        if(ch[x] == '(') {
            update(1, 1, n, x, n, -2);
            ch[x] = ')';
            close.insert(x);
            x = *close.begin();
            res[i] = x;
            ch[x] = '(';
            update(1, 1, n, x, n, +2);
            close.erase(x);
        }
        else {
            update(1, 1, n, x, n, +2);
            close.erase(x);
            ch[x] = '(';
            x = query(1, 1, n) + 1;
            ch[x] = ')';
            update(1, 1, n, x, n, -2);
            close.insert(x);
            res[i] = x;
        }
    }
    Rep(i, qr) printf("%d\n", res[i]);
    return 0;
}


### Prompt

Develop a solution in Cpp to the problem described below:

Example

Input

6 3
((()))
4
3
1


Output

2
2
1

### Response

```cpp
/**
Zubayet Zaman Zico

codeforces : I_See_You
hackerrank : I_See_You
codechef   : xico
spoj       : xico
email      : hhoho07@gmail.com
**/

//#include <stdio.h>
//#include <iostream>
//#include <cstring>
//#include <cmath>
//#include <algorithm>
//#include <string>
//#include <vector>
//#include <map>
//#include <set>
//#include <queue>
//#include <cstdlib>
//#include <limits>
//#include <iostream>
//#include <sstream>
//#include <unordered_set>
//#include <unordered_map>
//#include <random>
#include <bits/stdc++.h>
//#include <ext/pb_ds/assoc_container.hpp>
//using namespace __gnu_pbds;
using namespace std;


//#define gc getchar unlocked
//#ifndef ONLINE JUDGE
#define gc getchar
//#endif // ONLINE JUDGE

//#define pc putchar_unlocked
//#ifndef ONLINE JUDGE
#define pc putchar
//#endif // ONLINE JUDGE

#define fRead           freopen("input.txt","r",stdin)
#define fWrite          freopen("output.txt","w",stdout)

#define eps             1e-9
#define inf             0x3f3f3f3f
#define INF             2e18
#define LL              long long
#define ULL             unsigned long long
#define PI              acos(-1.0)
#define pb              push_back
#define mk              make_pair
#define pii             pair<int,int>
#define pLL             pair<LL,LL>
#define ff              first
#define ss              second
#define all(a)          a.begin(),a.end()
#define rall(a)         a.rbegin(),a.rend()
#define SQR(a)          ((a)*(a))
#define Unique(a)       sort(all(a)),a.erase(unique(all(a)),a.end())
#define min3(a,b,c)     min(a,min(b,c))
#define max3(a,b,c)     max(a,max(b,c))
#define min4(a,b,c,d)   min(min(a,b),min(c,d))
#define max4(a,b,c,d)   max(max(a,b),max(c,d))
#define max5(a,b,c,d,e) max(max3(a,b,c),max(d,e))
#define min5(a,b,c,d,e) min(min3(a,b,c),min(d,e))
#define Iterator(a)     __typeof__(a.begin())
#define rIterator(a)    __typeof__(a.rbegin())
#define FOR(a,it)       for(Iterator(a) it = a.begin();it != a.end(); it++)
#define rFOR(a,it)      for(rIterator(a) it = a.rbegin();it != a.rend(); it++)
#define FastRead        ios_base::sync_with_stdio(0);cin.tie(0)
#define CasePrint       pc('C'); pc('a'); pc('s'); pc('e'); pc(' '); write(qq++,false); pc(':'); pc(' ')
#define vi              vector <int>
#define vL              vector <LL>
#define For(I,A,B)      for(int I = (A); I  < (B); ++I)
#define rFor(I,A,B)     for(int I = (A); I >= (B); --I)
#define Rep(I,N)        For(I,0,N)
#define REP(I,N)        For(I, 1, N + 1)
#define gti             int, vi, greater<int>
#define gtL             LL, vL, greater<LL>
#define Found(a, b)     a.find(b) != a.end()
#define y0              y00

const int MOD = 1e9 + 7;
int fx[] = {-1,+0,+1,+0,+1,+1,-1,-1,+0};
int fy[] = {+0,-1,+0,+1,+1,-1,+1,-1,+0};
int day[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
//template <typename T> using orderset = tree <T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>; // find_by_order, order_of_key
template <typename T> inline bool isLeap(T y) {return (y % 400 == 0) || (y % 100 ? y % 4 == 0 : false); }
template <typename T> inline T GCD (T a,T b ) {a = abs(a);b = abs(b); if(a < b) swap(a, b); while ( b ) { a = a % b; swap ( a, b ); } return a;}
template <typename T> inline T EGCD(T a,T b,T &x,T &y){if(a == 0) {x = 0;y = 1;return b;}T x1, y1;T d = EGCD(b % a, a, x1, y1);x = y1 - (b / a) * x1;y = x1;return d;}
template <typename T> inline T LCM(T x,T y){T tp = GCD(x,y);if( (x / tp) * 1. * y > 9e18) return 9e18;return (x / tp) * y;}
template <typename T> inline T BigMod(T A,T B,T M = MOD){A %= M;T ret = 1;while(B){if(B & 1) ret = (ret * A) % M;A = (A * A) % M;B = B >> 1;}return ret;}
template <typename T> inline T InvMod (T A,T M = MOD){return BigMod(A,M-2,M);}
template <typename T> void Compress(T * in, int n, int f = 0){vector <T> vv;for(int i = f; i < n + f; i++) vv.pb(in[i]);Unique(vv);for(int i = f; i < n + f; i++) in[i] = lower_bound(all(vv), in[i]) - vv.begin();}
//template <typename T> void Compress(vector <T> &in){vector <T> vv;for(T x : in) vv.pb(x);Unique(vv);for(int i = 0; i < in.size(); i++) in[i] = lower_bound(all(vv), in[i]) - vv.begin();}
/*---------------------------fast I/O------------------------------------*/
#define scani2(a,b) scani(a) , scani(b)
#define scani3(a,b,c) scani(a), scani(b), scani(c)
#define scani4(a,b,c,d) scani(a), scani(b), scani(c), scani(d)
#define scani5(a,b,c,d,e) scani(a), scani(b), scani(c), scani(d) , scani(e)
template <typename T> T scani(T &n){n = 0;bool negative = false;char c = gc();while( c < '0' || c > '9'){if(c == '-') negative = true;c = gc();}while(c >= '0' && c <= '9'){n = n*10 + c-48;c = gc();}if(negative) n = ~(n-1);return n;}
template <typename T> void write(T n,int type = true){if(n<0) {pc('-');n = -n;}if(!n) {pc('0');if(type==32) pc(' '); else if(type) pc('\n'); return;}char buff[22];int len = 0;while(n) buff[len++] = n%10+48,n/=10;for(int i=len-1;i>=0;i--) pc(buff[i]);if(type==32) pc(' '); else if(type) pc('\n');}
int scans(char *a){int i=0;char c = 0;while(c < 33) c = gc();while(c > 33){a[i++] = c;c = gc();}a[i] = 0;return i;}
/*********************************************** End of template *********************************************/


#ifdef Sieve
const int pSz = 2000006;
bool np[pSz + 10]; vi prime; int prime_size;void sieve(){np[0] = np[1] = 1;prime.pb(2);for(LL i = 4; i <= pSz; i+=2) np[i] = 1;for(LL i = 3; i <= pSz; i+=2){if(!np[i]){prime.pb(i);for(LL j = i * i; j <= pSz; j += (i << 1)) np[j] = 1;}}prime_size = prime.size();}
#endif

#ifdef Combi
const int nSz = 2000006;
LL F[nSz + 1], tMod = MOD;
void Factorial(){ F[0] = 1; for(int i = 1; i <= nSz; i++) F[i] = (F[i - 1] * i) % tMod; }
inline LL nCr(int n, int r) { if(n < r) return 0; return (F[n] * InvMod((F[n - r] * F[r]) % tMod, tMod)) % tMod; }

#endif

#ifdef Z_Algo
void zAlgo(char *s, int *z){
    int L, R, sz; sz = strlen(s); z[0] = L = R = 0;
    For(i, 1, sz) { z[i] = 0; if(i <= R) z[i] = min(z[i - L], R - i + 1); while(i + z[i] < sz && s[i + z[i]] == s[z[i]]) z[i]++; if(i + z[i] - 1 > R) L = i, R = i + z[i] - 1; }
}void zAlgo(string &s, int *z){
    int L, R, sz; sz = s.size(); z[0] = L = R = 0;
    For(i, 1, sz) { z[i] = 0; if(i <= R) z[i] = min(z[i - L], R - i + 1); while(i + z[i] < sz && s[i + z[i]] == s[z[i]]) z[i]++; if(i + z[i] - 1 > R) L = i, R = i + z[i] - 1; }
}void zAlgo(int *s, int *z, int n){
    int L, R, sz; sz = n; z[0] = L = R = 0;
    For(i, 1, sz) { z[i] = 0; if(i <= R) z[i] = min(z[i - L], R - i + 1); while(i + z[i] < sz && s[i + z[i]] == s[z[i]]) z[i]++; if(i + z[i] - 1 > R) L = i, R = i + z[i] - 1; }
}
#endif // Z_Algo


/********************************************* define Template *************************************************/

template <typename T> inline T SqrDis(T x1, T y1, T x2, T y2){return SQR(x1 - x2) + SQR(y1 - y2);}
template <typename T> inline T Area2(T Ax, T Ay, T Bx, T By, T Cx, T Cy){T ret = Ax * (By - Cy) + Bx * (Cy - Ay) + Cx * (Ay - By);
    if(ret < 0) return ret = -ret;
    return ret;
}
/**************************************************** GEO ******************************************************/
const int N = 2000006; /** need to update this **/
const int M = 2097152 + 10;
const ULL hs = 3797;
/** use data types carefully try to take 'long long' **/
const int base = 555;

set <int> close;
int Tree[N << 2], Pr[N << 2], cum[N];
int n, qr;
char ch[N];

void push_down(int node, int b, int e){
    if(Pr[node] == 0 || b == e) return ;
    int mid = b + e >> 1;
    int lf = node << 1;
    int rt = lf | 1;

    Pr[lf] += Pr[node];
    Pr[rt] += Pr[node];
    Tree[lf] += Pr[node];
    Tree[rt] += Pr[node];

    Pr[node] = 0;
}

void built(int node, int b, int e) {
    if(b == e) {
        Tree[node] = cum[b];
        return ;
    }
    int mid = b + e >> 1;
    int lf = node << 1;
    int rt = lf | 1;
    built(lf, b, mid);
    built(rt, mid + 1, e);
    Tree[node] = min(Tree[lf], Tree[rt]);
}

void update(int node, int b, int e, int i, int j, int v) {
    push_down(node, b, e);
    if(b > j || e < i) return ;
    if(b >= i && e <= j){
        Tree[node] += v;
        Pr[node] += v;
        return ;
    }
    int mid = b + e >> 1;
    int lf = node << 1;
    int rt = lf | 1;
    update(lf, b, mid, i, j, v);
    update(rt, mid + 1, e, i, j, v);
    Tree[node] = min(Tree[lf], Tree[rt]);
}

int query(int node, int b, int e){
    push_down(node, b, e);
    if(b == e) return b;
    int mid = b + e >> 1;
    int lf = node << 1;
    int rt = lf | 1;
//    cout << node << ' ' << b << ' ' << e << ' ' << Tree[lf] << ' ' << Tree[rt] << '\n';
    if(Tree[rt] >= 2) return query(lf, b, mid);
    return query(rt, mid + 1, e);
}

int res[N];

int main()
{
    scanf("%d %d", &n, &qr);
    scanf("%s", ch + 1);
    For(i, 1, n + 1) {
        cum[i] += cum[i - 1];
        if(ch[i] == '(') {
            cum[i]++;
        }
        else {
            cum[i]--;
            close.insert(i);
        }
    }

    built(1, 1, n);
    Rep(i, qr) {
        int x; scanf("%d", &x);
        if(ch[x] == '(') {
            update(1, 1, n, x, n, -2);
            ch[x] = ')';
            close.insert(x);
            x = *close.begin();
            res[i] = x;
            ch[x] = '(';
            update(1, 1, n, x, n, +2);
            close.erase(x);
        }
        else {
            update(1, 1, n, x, n, +2);
            close.erase(x);
            ch[x] = '(';
            x = query(1, 1, n) + 1;
            ch[x] = ')';
            update(1, 1, n, x, n, -2);
            close.insert(x);
            res[i] = x;
        }
    }
    Rep(i, qr) printf("%d\n", res[i]);
    return 0;
}


```