不是特别懂题目意思，不追求AC，至少拿到暴力的分

#include<bits/stdc++.h>
using namespace std;
int n,k,ans;
string s;
vector<string>a;
bool pp(string c){
	int a=0,b=0;
	for(int i=0;i<c.size();i++){	
		b+=c[i]==')';
		if(b>a)return 0;
		a+=c[i]=='(';
	}
	return a==b&&c[c.size()-1]!='*'&&c[0]!='*';
}
bool xz(string c){
	for(int i=0;i<c.size()-4;i++){
		if(c[i]=='('&&c[i+1]=='*'&&c[i+2]=='*'&&c[i+3]=='(')return 0;
		if(c[i]==')'&&c[i+1]=='*'&&c[i+2]=='*'&&c[i+3]==')')return 0;
	}
	//for(int i=0;i<c.size()-2;i++){
		//if(c[i]=='')
	//}
	return 1;
}
void ff(){
	cin>>n>>k>>s;
	clock_t cl=clock();
	for(int i=0;i<100000;i++){
		string c=s;
		while(count(c.begin(),c.end(),'?')>0){
			int b=-1;
			while(b<0||(c[b]!='?'&&c[b]!='('&&c[b]!=')'))
				b=rand()%(s.size());
			int d=rand()%3;
			if(d==0)
				c[b]='(';
			else if(d==1)
				c[b]=')';
			else
				c[b]='*';
		}
		//cout<<c<<" "<<pp(c)<<"-";
		if(pp(c)&&count(c.begin(),c.end(),'*')==k&&xz(c))
			if(!count(a.begin(),a.end(),c))
				ans++,
				a.push_back(c);//cout<<c<<"\n";	
		if(clock()-cl>CLOCKS_PER_SEC*1.5)return;
		
	}
}
int main(){
	ff();
	cout<<ans;
	return 0;
}