#include <bits/stdc++.h>
#define inf 1000000007
#define mod 1000000007
// #define int long long
// #pragma GCC optimize("Ofast","inline","-ffast-math")
// #pragma GCC target("avx,sse2,sse3,sse4,mmx")
using namespace std;
template <typename T> void read(T &x){
	x=0;char ch=getchar();int fh=1;
	while (ch<'0'||ch>'9'){if (ch=='-')fh=-1;ch=getchar();}
	while (ch>='0'&&ch<='9')x=x*10+ch-'0',ch=getchar();
	x*=fh;
}
template <typename T> void write(T x) {
	if (x<0) x=-x,putchar('-');
	if (x>9) write(x/10);
	putchar(x%10+'0');
}
template <typename T> void writeln(T x) {
	write(x);
	puts("");
}
const double eps=1e-7;
int n,q;
int x[5005],y[5005];
signed main()
{
	// freopen(".in","r",stdin);
	// freopen(".out","w",stdout);
	read(n);read(q);
	for(int i=1;i<=n;++i)
		read(x[i]),read(y[i]);
	while(q--)
	{
		int xa,ya,xb,yb;
		read(xa);read(ya);read(xb);read(yb);
		double xc=(xa+xb)/2.0,yc=(ya+yb)/2.0;
		int fh=0;
		bool inch=1;
		for(int i=1;i<=n;++i)
		{
			int j=(i<n?i+1:1);
			double s=(x[i]-xc)*(y[j]-yc)-(x[j]-xc)*(y[i]-yc);
			if(fabs(s)<eps) fh=-1;
			if(fh==1&&s<-eps) inch=0;
			if(fh==-1&&s>eps) inch=0;
			if(fh==0) fh=(s>eps?1:s<-eps?-1:0);
		}
		if(inch)
		{
			printf("%.10lf\n",((xc-xa)*(xc-xa)+(yc-ya)*(yc-ya))/2);
			continue;
		}
		double mn=1e18;
		for(int i=1;i<=n;++i)
		{
			int j=(i<n?i+1:1);
			mn=min(mn,(x[i]-xc)*(x[i]-xc)+(y[i]-yc)*(y[i]-yc));
			mn=min(mn,(x[j]-xc)*(x[j]-xc)+(y[j]-yc)*(y[j]-yc));
			if(x[i]==x[j])
			{
				if(yc>min(y[i],y[j])-eps&&yc<max(y[i],y[j])+eps)
					mn=min(mn,(xc-x[i])*(xc-x[i]));
				continue;
			}
			if(y[i]==y[j])
			{
				if(xc>min(x[i],x[j])-eps&&xc<max(x[i],x[j])+eps)
					mn=min(mn,(yc-y[i])*(yc-y[i]));
				continue;
			}
			double k=(y[i]-y[j])*1.0/(x[i]-x[j]);
			double kk=-1/k;
			double b=y[i]-k*x[i],bb=yc-kk*xc;
			double xx=(b-bb)/(kk-k),yy=k*xx+b;
			if(xx>min(x[i],x[j])-eps&&xx<max(x[i],x[j])+eps)
				mn=min(mn,(xc-xx)*(xc-xx)+(yc-yy)*(yc-yy));
		}
		printf("%.10lf\n",mn+((xc-xa)*(xc-xa)+(yc-ya)*(yc-ya))/2);
	}
	return 0;
}