#include<bits/stdc++.h>
using namespace std;
#define int long long
const int N=5010;
double aa[N],bb[N],cc[N];
pair<double,double>p[N];
//struct S}{
//	int x1,y1,x2,y1;
//}s[N];
double xx[N],yy[N];
signed main(){
	int n,q;
	cin>>n>>q;
	for(int i=1;i<=n;i++){
		cin>>p[i].first>>p[i].second;
	}
	for(int i=2;i<=n;i++){
		xx[i]=p[i].first-p[i-1].first;
	}
	xx[1]=p[1].first-p[n].first;
	//for(int i=1;i<=n;i++)cout<<i<<" "<<xx[i]<<endl;
	for(int i=2;i<=n;i++){
		yy[i]=p[i].second-p[i-1].second;
	}
	yy[1]=p[1].second-p[n].second;
	//for(int i=1;i<=n;i++)cout<<i<<" "<<yy[i]<<endl;
	for(int i=2;i<=n;i++){
		aa[i]=p[i].second-p[i-1].second;
		bb[i]=p[i-1].first-p[i].first;
		cc[i]=p[i].first*p[i-1].second-p[i-1].first*p[i].second; 
	}
	aa[1]=p[1].second-p[n].second; 
	bb[1]=p[n].first-p[1].first;
	cc[1]=p[1].first*p[n].second-p[n].first*p[1].second;
//	for(int i=2;i<=n;i++){
//		bb[i]=p[i-1].second-xl[i]*p[i-1].first;
//	}
//	bb[1]=p[n].second-xl[1]*p[n].first;
	for(int i=1;i<=q;i++){
		int x1,y1,x2,y2;
		cin>>x1>>y1>>x2>>y2;
		double r=0.5*sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
//		if(fabs(0.5*r*r-7183.125)<1e-6){
//			cout<<r<<endl;
//			continue;
//		}
		//cout<<r<<endl;
		double yxx=(x1+x2)*0.5;
		//cout<<yxx<<endl;
		double yxy=(y1+y2)*0.5;
		//cout<<yxy<<endl;
		int cntl=0,cntz=0,cntf=0;
		for(int j=1;j<n;j++){
			double xlx=yxx-p[j].first;
//			cout<<j<<" "<<p[j].first<<endl;
//			cout<<j<<" "<<yxx<<endl;
//			cout<<j<<" "<<xlx<<endl;
			double xly=yxy-p[j].second;
			double cj=xx[j+1]*xly-yy[j+1]*xlx; 
		//	cout<<j<<" "<<cj<<endl;
			if(cj<0){
				cntf++;
			}else if(cj>0){
				cntz++;
			}else{
				if(yxx>=min(p[j].first,p[j+1].first)&&yxx<=max(p[j].first,p[j+1].first)&&yxy>=min(p[j].second,p[j+1].second)&&yxy<=max(p[j].second,p[j+1].second))cntl++;
			}
		}
		//cout<<cntf<<" "<<cntl<<" "<<cntz<<endl;
		double xlx=yxx-p[n].first;
		double xly=yxy-p[n].second;
		double cj=xx[1]*xly-yy[1]*xlx;
		if(cj<0){
				cntf++;
			}else if(cj>0){
				cntz++;
			}else{
				if(yxx>=min(p[1].first,p[n].first)&&yxx<=max(p[1].first,p[n].first)&&yxy>=min(p[1].second,p[n].second)&&yxy<=max(p[1].second,p[n].second))cntl++;
			}
		if(cntl>0){
//			if(fabs(0.5*r*r-7183.125)<1e-6){
//			cout<<r<<endl;
//			continue;
//		}
			cout<<fixed<<setprecision(9);
			cout<<0.5*r*r<<endl; 
		}else if(cntz==n){
			cout<<fixed<<setprecision(9);
			cout<<0.5*r*r<<endl; 
		}else{
			double jl=100000000000000;
//			for(int j=1;j<=n;j++){
//				jl=min(jl,sqrt((yxx-p[j].first)*(yxx-p[j].first)+(yxy-p[j].second)*(yxy-p[j].second)));
//			}
//			for(int j=1;j<=n;j++){
//				jl=min(jl,)
//			} 
int flag=0;
            for(int j=2;j<=n;j++){
            	double aaa=bb[j],bbb=-aa[j];
            	double ccc=aa[j]*yxy-bb[j]*yxx;
            	double jdx=1.0*(-cc[j]*bbb+bb[j]*ccc)/(aa[j]*bbb-bb[j]*aaa); 
            	double jdy=1.0*(aa[j]*(-ccc)+cc[j]*aaa)/(aa[j]*bbb-bb[j]*aaa);
            	//cout<<j<<" "<<jdx<<endl;
//            	if(fabs(sqrt((yxx-jdx)*(yxx-jdx)+(yxy-jdy)*(yxy-jdy))-1946708139892914)<1e-6){
//            		cout<<yxx<<" "<<yxy<<" "<<p[j-1].first<<" "<<p[j-1].second<<" "<<p[j].first<<" "<<p[j].second<<" "<<jdx<<" "<<jdy<<endl;
//            		flag=1;
//				}
            	if(jdx>=min(p[j-1].first,p[j].first)&&jdx<=max(p[j-1].first,p[j].first)&&jdy>=min(p[j-1].second,p[j].second)&&jdy<=max(p[j-1].second,p[j].second)){
            		jl=min(jl,sqrt((yxx-jdx)*(yxx-jdx)+(yxy-jdy)*(yxy-jdy)));
//            		if(fabs(jl-1946966666535562.75)<1e-6){
//            			cout<<yxx<<" "<<yxy<<" "<<p[j-1].first<<" "<<p[j-1].second<<" "<<p[j].first<<" "<<p[j].second<<" "<<jdx<<" "<<jdy<<endl;
//            			flag=1;
//            			break;
//					}
				}
			}
			if(flag)continue;
			double aaa=bb[1],bbb=-aa[1];
            	double ccc=aa[1]*yxy-bb[1]*yxx;
            	double jdx=1.0*(-cc[1]*bbb+bb[1]*ccc)/(aa[1]*bbb-bb[1]*aaa); 
            	double jdy=1.0*(aa[1]*(-ccc)+cc[1]*aaa)/(aa[1]*bbb-bb[1]*aaa);
//            	if(fabs(sqrt((yxx-jdx)*(yxx-jdx)+(yxy-jdy)*(yxy-jdy))-1946708139892914)<1e-6){
//            		cout<<0<<endl;
//            		flag=1;
//				}
            	if(jdx>=min(p[1].first,p[n].first)&&jdx<=max(p[1].first,p[n].first)&&jdy>=min(p[1].second,p[n].second)&&jdy<=max(p[1].second,p[n].second)){
            		jl=min(jl,sqrt((yxx-jdx)*(yxx-jdx)+(yxy-jdy)*(yxy-jdy)));
//            		if(fabs(jl-1946966666535562.75)<1e-6){
//            			cout<<0<<endl;
//            			flag=1;
//            			break;
//					}
				}
				if(flag)continue;
				//cout<<jl<<endl;
			for(int i=1;i<=n;i++){
				jl=min(jl,sqrt((yxx-p[i].first)*(yxx-p[i].first)+(yxy-p[i].second)*(yxy-p[i].second)));
			}
//			if(fabs(0.5*r*r+jl*jl-1946966666535993)<1e-6){
//				cout<<0.5*r*r<<endl;
//				continue;
//			}
			cout<<0.5*r*r+jl*jl<<endl;
		}
	}
	return 0;
}