#include<bits/stdc++.h>
#define irep(i,l,r) for(int i = l; i <= r; ++i)
#define drep(i,r,l) for(int i = r; i >= l; --i)
#define ceil(pp,qq) (((pp)>0)^((qq)>0)?-Abs(pp)/Abs(qq):(pp)%(qq)?(pp)/(qq)+1:(pp)/(qq))
#define floor(pp,qq) (((pp)>0)^((qq)>0)?-ceil(abs(pp),abs(qq)):(pp)/(qq))
#define ll long long
using namespace std;
ll Abs(ll x){return x > 0 ? x : - x;}
inline ll read(){
	char ch = getchar();
	ll s = 0; bool w = 0;
	while(!isdigit(ch)){if(ch == '-')w = 1;ch = getchar();}
	while(isdigit(ch))s = (s << 3) + (s << 1) + (ch ^ 48), ch = getchar();
	return w ? - s : s;
}

const int itinf = 2e9;
const ll llinf = 4e18;
const int mod = 1000000007;
const int N = 500009;
double eps = 1e-8;
struct point{
	double x, y;
	point(){}
	point(double xx, double yy){x = xx, y = yy;}
	double operator * (const point& p){
		return x * p.x + y * p.y;
	}
	double operator ^ (const point& p){
		return x * p.y - y * p.x;
	}
	point operator + (const point& p){
		point pp(x + p.x, y + p.y);
		return pp;
	}
	point operator - (const point& p){
		point pp(x - p.x, y - p.y);
		return pp;
	}
	

}a[N];
double len(point p){
		return p.x * p.x + p.y * p.y;
}
long double dis(point p1, point p2, point p){
	if((p - p2) * (p1 - p2) >= -eps && (p - p1) * (p2 - p1) >= -eps)
		return pow((p1 - p) ^ (p2 - p), 2 ) / len(p1 - p2);
	else return min(len(p - p1), len(p - p2));
}
int main(){
//	point s1(1,1),s2(1,-1),g(1,0);
//	cerr << dis(s1,s2,g) << endl;
	int n = read(), q = read();
	irep(i,1,n){
		int x = read(), y = read();
		point temp(x,y);
		a[i] = temp;
	}

	a[n + 1] = a[1];
	while(q --){
		double x1, y1, x2, y2;
		scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);
		point c(0.5 * (x1 + x2), 0.5 * (y1 + y2));
		double r = 0.125 * ((y2 - y1) * (y2 - y1) + (x2 - x1) * (x2 - x1));
		bool fl = 0;
	//	cerr << c.x << ' ' <<c.y << endl;
		for(int i = 1; i <= n; ++i){
		//	cerr << ((a[i + 1] - a[i]) ^ (c - a[i])) << endl;
			if(((a[i + 1] - a[i]) ^ (c - a[i])) < -eps){
				fl = 1;
				break;
			}
		}
		if(fl == 0){
			printf("%0.12lf\n", r);
			continue;
		}
		long double ans = 1e24;
		for(int i = 1; i <= n; ++i){
			ans = min(dis(a[i],a[i+1],c),ans);//	cerr << dis(a[i],a[i+1],c) << ' ';
		}		
		//cerr << endl;
		printf("%0.12Lf\n", r + ans);
	}
	return 0;
}