#include<iostream>
#include<queue>
using namespace std;
#include<vector>
#include<functional>
template<typename T>
struct lazysegtree{
	using F=function<T(T,T)>;
	using G=function<T(T,T,int,int)>;
	const F calcfn,lazycalcfn;
	const G updatefn;
	int n;
	T defvalue,lazydefvalue;
	vector<T>dat,lazy;
	vector<bool>lazyflag;
	lazysegtree(int n_=0,T defvalue_=0,
		const F calcfn_=[](T a,T b){return a+b;},
		const F lazycalcfn_=[](T a,T b){return a+b;},
		const G updatefn_=[](T a,T b,int l,int r){return a+b*(r-l);},
		T lazydefvalue_=0
	):defvalue(defvalue_),lazydefvalue(lazydefvalue_),
		calcfn(calcfn_),lazycalcfn(lazycalcfn_),updatefn(updatefn_)
	{
		n=1;
		while(n<n_)n<<=1;
		dat.assign(2*n-1,defvalue);
		lazy.assign(2*n-1,lazydefvalue);
		lazyflag.assign(2*n-1,false);
	}
	void copy(const vector<T>&v)
	{
		for(int i=0;i<v.size();i++)dat[i+n-1]=v[i];
		for(int i=n-2;i>=0;i--)dat[i]=calcfn(dat[2*i+1],dat[2*i+2]);
	}
	void eval(int i,int l,int r)
	{
		if(lazyflag[i])
		{
			dat[i]=updatefn(dat[i],lazy[i],l,r);
			if(r-l>1)
			{
				lazy[2*i+1]=lazycalcfn(lazy[2*i+1],lazy[i]);
				lazy[2*i+2]=lazycalcfn(lazy[2*i+2],lazy[i]);
				lazyflag[2*i+1]=lazyflag[2*i+2]=true;
			}
			lazy[i]=lazydefvalue;
			lazyflag[i]=false;
		}
	}
	void update(int a,int b,T x,int k=0,int l=0,int r=-1)//[a,b)
	{
		if(r<0)r=n;
		eval(k,l,r);
		if(b<=l||r<=a)return;
		else if(a<=l&&r<=b)
		{
			lazy[k]=lazycalcfn(lazy[k],x);
			lazyflag[k]=true;
			eval(k,l,r);
		}
		else
		{
			update(a,b,x,2*k+1,l,(l+r)/2);
			update(a,b,x,2*k+2,(l+r)/2,r);
			dat[k]=calcfn(dat[2*k+1],dat[2*k+2]);
		}
	}
	T query(int a,int b,int k=0,int l=0,int r=-1)//[a,b)
	{
		if(r<0)r=n;
		eval(k,l,r);
		if(b<=l||r<=a)return defvalue;
		else if(a<=l&&r<=b)return dat[k];
		else return calcfn(
			query(a,b,2*k+1,l,(l+r)/2),
			query(a,b,2*k+2,(l+r)/2,r)
		);
	}
};
string s;
int N,Q;
int main()
{
	cin>>N>>Q>>s;
	priority_queue<int>X;
	lazysegtree<pair<int,int> >P(N+1,make_pair(2*N,2*N),
	[](pair<int,int>a,pair<int,int>b){return a<b?a:b;},
	[](pair<int,int>a,pair<int,int>b){return make_pair(a.first+b.first,0);},
	[](pair<int,int>a,pair<int,int>b,int l,int r){return make_pair(a.first+b.first,a.second);},
	make_pair(0,0));
	vector<pair<int,int> >init(N+1);
	init[0]=make_pair(0,1);
	for(int i=0;i<N;i++)
	{
		init[i+1].first=init[i].first;
		init[i+1].second=-i;
		if(s[i]=='(')init[i+1].first++;
		else
		{
			init[i+1].first--;
			X.push(-i);
		}
	}
	P.copy(init);
	for(;Q--;)
	{
		int id;cin>>id;
		id--;
		if(s[id]=='(')
		{
			s[id]=')';
			X.push(-id);
			while(s[-X.top()]=='(')X.pop();
			int jd=-X.top();
			cout<<jd+1<<endl;
			s[jd]='(';
			P.update(jd+1,id+1,make_pair(2,0));
		}
		else
		{
			s[id]='(';
			int jjd=1-P.query(0,id+1).second;
			int jd=1-P.query(jjd+1,id+1).second;
			cout<<jd+1<<endl;
			s[jd]=')';
			X.push(-jd);
			P.update(jd+1,id+1,make_pair(-2,0));
		}
	}
}


### Prompt

Create a solution in cpp for the following problem:

Example

Input

6 3
((()))
4
3
1


Output

2
2
1

### Response

```cpp
#include<iostream>
#include<queue>
using namespace std;
#include<vector>
#include<functional>
template<typename T>
struct lazysegtree{
	using F=function<T(T,T)>;
	using G=function<T(T,T,int,int)>;
	const F calcfn,lazycalcfn;
	const G updatefn;
	int n;
	T defvalue,lazydefvalue;
	vector<T>dat,lazy;
	vector<bool>lazyflag;
	lazysegtree(int n_=0,T defvalue_=0,
		const F calcfn_=[](T a,T b){return a+b;},
		const F lazycalcfn_=[](T a,T b){return a+b;},
		const G updatefn_=[](T a,T b,int l,int r){return a+b*(r-l);},
		T lazydefvalue_=0
	):defvalue(defvalue_),lazydefvalue(lazydefvalue_),
		calcfn(calcfn_),lazycalcfn(lazycalcfn_),updatefn(updatefn_)
	{
		n=1;
		while(n<n_)n<<=1;
		dat.assign(2*n-1,defvalue);
		lazy.assign(2*n-1,lazydefvalue);
		lazyflag.assign(2*n-1,false);
	}
	void copy(const vector<T>&v)
	{
		for(int i=0;i<v.size();i++)dat[i+n-1]=v[i];
		for(int i=n-2;i>=0;i--)dat[i]=calcfn(dat[2*i+1],dat[2*i+2]);
	}
	void eval(int i,int l,int r)
	{
		if(lazyflag[i])
		{
			dat[i]=updatefn(dat[i],lazy[i],l,r);
			if(r-l>1)
			{
				lazy[2*i+1]=lazycalcfn(lazy[2*i+1],lazy[i]);
				lazy[2*i+2]=lazycalcfn(lazy[2*i+2],lazy[i]);
				lazyflag[2*i+1]=lazyflag[2*i+2]=true;
			}
			lazy[i]=lazydefvalue;
			lazyflag[i]=false;
		}
	}
	void update(int a,int b,T x,int k=0,int l=0,int r=-1)//[a,b)
	{
		if(r<0)r=n;
		eval(k,l,r);
		if(b<=l||r<=a)return;
		else if(a<=l&&r<=b)
		{
			lazy[k]=lazycalcfn(lazy[k],x);
			lazyflag[k]=true;
			eval(k,l,r);
		}
		else
		{
			update(a,b,x,2*k+1,l,(l+r)/2);
			update(a,b,x,2*k+2,(l+r)/2,r);
			dat[k]=calcfn(dat[2*k+1],dat[2*k+2]);
		}
	}
	T query(int a,int b,int k=0,int l=0,int r=-1)//[a,b)
	{
		if(r<0)r=n;
		eval(k,l,r);
		if(b<=l||r<=a)return defvalue;
		else if(a<=l&&r<=b)return dat[k];
		else return calcfn(
			query(a,b,2*k+1,l,(l+r)/2),
			query(a,b,2*k+2,(l+r)/2,r)
		);
	}
};
string s;
int N,Q;
int main()
{
	cin>>N>>Q>>s;
	priority_queue<int>X;
	lazysegtree<pair<int,int> >P(N+1,make_pair(2*N,2*N),
	[](pair<int,int>a,pair<int,int>b){return a<b?a:b;},
	[](pair<int,int>a,pair<int,int>b){return make_pair(a.first+b.first,0);},
	[](pair<int,int>a,pair<int,int>b,int l,int r){return make_pair(a.first+b.first,a.second);},
	make_pair(0,0));
	vector<pair<int,int> >init(N+1);
	init[0]=make_pair(0,1);
	for(int i=0;i<N;i++)
	{
		init[i+1].first=init[i].first;
		init[i+1].second=-i;
		if(s[i]=='(')init[i+1].first++;
		else
		{
			init[i+1].first--;
			X.push(-i);
		}
	}
	P.copy(init);
	for(;Q--;)
	{
		int id;cin>>id;
		id--;
		if(s[id]=='(')
		{
			s[id]=')';
			X.push(-id);
			while(s[-X.top()]=='(')X.pop();
			int jd=-X.top();
			cout<<jd+1<<endl;
			s[jd]='(';
			P.update(jd+1,id+1,make_pair(2,0));
		}
		else
		{
			s[id]='(';
			int jjd=1-P.query(0,id+1).second;
			int jd=1-P.query(jjd+1,id+1).second;
			cout<<jd+1<<endl;
			s[jd]=')';
			X.push(-jd);
			P.update(jd+1,id+1,make_pair(-2,0));
		}
	}
}


```