#include<bits/stdc++.h>
#define int long long
#define mod 998244353ll
#define pii pair<db,db>
#define fi first
#define se second
#define mems(x,y) memset(x,y,sizeof(x))
#define pb push_back
#define db double
using namespace std;
const int maxn=200010;
const int inf=2e18;
const db eps=1e-8;
inline int read(){
	int x=0,f=1;
	char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=(x<<3)+(x<<1)+(ch-48);ch=getchar();}
	return x*f;
}
bool Mbe;

int n,q;
pii a[maxn];
db cross(pii u,pii v){return u.fi*v.se-u.se*v.fi;}
db mul(pii u,pii v){return u.fi*v.fi+u.se*v.se;}
pii operator-(pii u,pii v){return {u.fi-v.fi,u.se-v.se};}
db dis(pii u,pii v){return sqrtl((u.fi-v.fi)*(u.fi-v.fi)+(u.se-v.se)*(u.se-v.se));}
db area(pii u,pii v,pii w){return abs(u.fi*v.se+v.fi*w.se+w.fi*u.se-u.fi*w.se-v.fi*u.se-w.fi*v.se)/2;}
db dis(pii u,pii v,pii w){
	db d=abs(area(u,v,w))*2/dis(v,w);
	// cout<<d<<" "<<dis(u,v)<<" "<<dis(u,w)<<"\n";
	if(mul(u-w,v-w)<-eps||mul(u-v,w-v)<-eps)return min(dis(u,v),dis(u,w));
	return d;
}
void work(){
	n=read();q=read();
	for(int i=1;i<=n;i++)a[i]={read(),read()};a[n+1]=a[1];
	while(q--){
		pii b={read(),read()},c={read(),read()};
		pii o={(b.fi+c.fi)/2,(b.se+c.se)/2};
		db r=dis(o,b);
		db ans=inf;
		for(int i=1;i<=n;i++){
			ans=min(ans,dis(o,a[i],a[i+1]));
			// cout<<i<<" "<<ans<<"\n";
		}
		bool fl=1;
		for(int i=1;i<=n;i++)if(cross(a[i+1]-a[i],o-a[i])<-eps)fl=0;
		if(fl)ans=0;
		// cout<<r<<" "<<ans<<" "<<fl<<"\n";
		printf("%.10lf\n",r*r/2+ans*ans);
	}
}

// \
444

bool Med;
int T;
signed main(){
//	freopen(".in","r",stdin);
//	freopen(".out","w",stdout);
	
//	ios::sync_with_stdio(0);
//	cin.tie(0);cout.tie(0);
	
//	cerr<<(&Mbe-&Med)/1048576.0<<" MB\n";
	
	T=1;
	while(T--)work();
}