#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-10;
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);
			double dis=sqrtl((x[i]-x[j])*(x[i]-x[j])+(y[i]-y[j])*(y[i]-y[j]));
			double l=0,r=dis;
			while(r-l>eps)
			{
				double lmid=(2*l+r)/3,rmid=(l+2*r)/3;
				double ld=(x[i]+(x[j]-x[i])/dis*lmid-xc)*(x[i]+(x[j]-x[i])/dis*lmid-xc)+(y[i]+(y[j]-y[i])/dis*lmid-yc)*(y[i]+(y[j]-y[i])/dis*lmid-yc);
				double rd=(x[i]+(x[j]-x[i])/dis*rmid-xc)*(x[i]+(x[j]-x[i])/dis*rmid-xc)+(y[i]+(y[j]-y[i])/dis*rmid-yc)*(y[i]+(y[j]-y[i])/dis*rmid-yc);
				mn=min({mn,ld,rd});
				if(ld<rd) r=rmid;
				else l=lmid;
			}
		}
		printf("%.10lf\n",mn+((xc-xa)*(xc-xa)+(yc-ya)*(yc-ya))/2);
	}
	return 0;
}