#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif

#include <bits/stdc++.h>
using namespace std;

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif

using uint=unsigned;
using ull=unsigned long long;

template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
	return os<<vc<t>(all(a));
}

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

pi readpi(int off=0){
	int a,b;cin>>a>>b;
	return pi(a+off,b+off);
}

template<class t>
void print_single(t x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

template<class t,class u>
void print_single(const pair<t,u>&p,int suc=1){
	print_single(p.a,2);
	print_single(p.b,suc);
}

template<class T>
void print_single(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print_single(v[i],i==int(v.size())-1?suc:2);
}

template<class T>
void print_offset(const vector<T>&v,ll off,int suc=1){
	rep(i,v.size())
		print_single(v[i]+off,i==int(v.size())-1?suc:2);
}

template<class T,size_t N>
void print_single(const array<T,N>&v,int suc=1){
	rep(i,N)
		print_single(v[i],i==int(N)-1?suc:2);
}

template<class T>
void print(const T&t){
	print_single(t);
}

template<class T,class ...Args>
void print(const T&t,const Args&...args){
	print_single(t,2);
	print(args...);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

void YES(bool ex=true){
	cout<<"YES\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void NO(bool ex=true){
	cout<<"NO\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void Yes(bool ex=true){
	cout<<"Yes\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void No(bool ex=true){
	cout<<"No\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
//#define CAPITAL
/*
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<"\n";
	#else
	cout<<"Yes"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<"\n";
	#else
	cout<<"No"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}*/
void possible(bool ex=true){
	#ifdef CAPITAL
	cout<<"POSSIBLE"<<"\n";
	#else
	cout<<"Possible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void impossible(bool ex=true){
	#ifdef CAPITAL
	cout<<"IMPOSSIBLE"<<"\n";
	#else
	cout<<"Impossible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int topbit(ull t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int botbit(ull a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
int popcount(ull t){
	return __builtin_popcountll(t);
}
int bitparity(ll t){
	return __builtin_parityll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
ll mask(int i){
	return (ll(1)<<i)-1;
}
ull umask(int i){
	return (ull(1)<<i)-1;
}
ll minp2(ll n){
	if(n<=1)return 1;
	else return ll(1)<<(topbit(n-1)+1);
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
	//#ifdef LOCAL
	static mt19937_64 gen;
	/*#else
	static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
	#endif*/
	return uniform_int_distribution<ll>(l, r)(gen);
}

ll rand_int(ll k){ //[0,k)
	return rand_int(0,k-1);
}

template<class t>
void myshuffle(vc<t>&a){
	rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}

template<class t>
int lwb(const vc<t>&v,const t&a){
	return lower_bound(all(v),a)-v.bg;
}
template<class t>
bool bis(const vc<t>&v,const t&a){
	return binary_search(all(v),a);
}

vvc<int> readGraph(int n,int m){
	vvc<int> g(n);
	rep(i,m){
		int a,b;
		cin>>a>>b;
		//sc.read(a,b);
		a--;b--;
		g[a].pb(b);
		g[b].pb(a);
	}
	return g;
}

vvc<int> readTree(int n){
	return readGraph(n,n-1);
}

vc<ll> presum(const vi&a){
	vc<ll> s(si(a)+1);
	rep(i,si(a))s[i+1]=s[i]+a[i];
	return s;
}
//BIT で数列を管理するときに使う (CF850C)
template<class t>
vc<t> predif(vc<t> a){
	gnr(i,1,si(a))a[i]-=a[i-1];
	return a;
}
template<class t>
vvc<ll> imos(const vvc<t>&a){
	int n=si(a),m=si(a[0]);
	vvc<ll> b(n+1,vc<ll>(m+1));
	rep(i,n)rep(j,m)
		b[i+1][j+1]=b[i+1][j]+b[i][j+1]-b[i][j]+a[i][j];
	return b;
}

//verify してないや
void transvvc(int&n,int&m){
	swap(n,m);
}
template<class t,class... Args>
void transvvc(int&n,int&m,vvc<t>&a,Args&...args){
	assert(si(a)==n);
	vvc<t> b(m,vi(n));
	rep(i,n){
		assert(si(a[i])==m);
		rep(j,m)b[j][i]=a[i][j];
	}
	a.swap(b);
	transvvc(n,m,args...);
}
//CF854E
void rotvvc(int&n,int&m){
	swap(n,m);
}
template<class t,class... Args>
void rotvvc(int&n,int&m,vvc<t>&a,Args&...args){
	assert(si(a)==n);
	vvc<t> b(m,vi(n));
	rep(i,n){
		assert(si(a[i])==m);
		rep(j,m)b[m-1-j][i]=a[i][j];
	}
	a.swap(b);
	rotvvc(n,m,args...);
}

//ソートして i 番目が idx[i]
//CF850C
template<class t>
vi sortidx(const vc<t>&a){
	int n=si(a);
	vi idx(n);iota(all(idx),0);
	sort(all(idx),[&](int i,int j){return a[i]<a[j];});
	return idx;
}
//vs[i]=a[idx[i]]
//例えば sortidx で得た idx を使えば単にソート列になって返ってくる
//CF850C
template<class t>
vc<t> a_idx(const vc<t>&a,const vi&idx){
	int n=si(a);
	assert(si(idx)==n);
	vc<t> vs(n);
	rep(i,n)vs[i]=a[idx[i]];
	return vs;
}
//CF850C
vi invperm(const vi&p){
	int n=si(p);
	vi q(n);
	rep(i,n)q[p[i]]=i;
	return q;
}

template<class t,class s=t>
s SUM(const vc<t>&a){
	return accumulate(all(a),s(0));
}

template<class t>
t MAX(const vc<t>&a){
	return *max_element(all(a));
}

template<class t>
t MIN(const vc<t>&a){
	return *min_element(all(a));
}

template<class t,class u>
pair<t,u> operator+(const pair<t,u>&a,const pair<t,u>&b){
	return mp(a.a+b.a,a.b+b.b);
}

vi vid(int n){
	vi res(n);iota(all(res),0);
	return res;
}

template<class S>
S getrev(S s){
	reverse(all(s));
	return s;
}

pi operator+(pi a,pi b){return pi(a.a+b.a,a.b+b.b);}

template<class t>
t gpp(vc<t>&vs){
	assert(si(vs));
	t res=move(vs.back());
	vs.pop_back();
	return res;
}

//copied from yosupo's library
//ptARTLY VERIFIED

//USACO 2022 January ptlatinum C

//#define GEOF

#ifdef GEOF
using ld=long double;
//using ld=double;
const ld PI=acos(ld(-1));
#else
using ld=ll;
#endif
const ld eps=1e-9;
int sgn(ld a){return a<-eps?-1:(a>eps?1:0);}
int sgn(ld a,ld b){return sgn(a-b);}
/*
using pt=complex<ld>;
#define x real()
#define y imag()
*/
struct pt {
    ld x,y;
    //pt(ld _x = ld(0), ld _y = ld(0)) : x(_x), y(_y) {}
    pt():x(0),y(0){}
    pt(ld xx,ld yy):x(xx),y(yy){}
    pt operator+(const pt& r) const { return {x + r.x, y + r.y}; }
    pt operator-(const pt& r) const { return {x - r.x, y - r.y}; }
    pt operator*(const pt& r) const {
        return {x * r.x - y * r.y, x * r.y + y * r.x};
    }
    pt inv()const{
		ld d=norm();
		return {x/d,-y/d};
	}
    pt operator/(const pt&r)const{
		return operator*(r.inv());
	}

    pt operator*(const ld& r) const { return {x * r, y * r}; }
    pt operator/(const ld& r) const { return {x / r, y / r}; }

    pt& operator+=(const pt& r) { return *this = *this + r; }
    pt& operator-=(const pt& r) { return *this = *this - r; }
    pt& operator*=(const pt& r) { return *this = *this * r; }
    pt& operator/=(const pt& r) { return *this = *this / r; }
    pt& operator*=(const ld& r) { return *this = *this * r; }
    pt& operator/=(const ld& r) { return *this = *this / r; }

    pt operator-() const { return {-x, -y}; }

	static int cmp(const pt&a,const pt&b){
		int v=sgn(a.x,b.x);
		return v?v:sgn(a.y,b.y);
	}
    bool operator<(const pt& r) const {
        return cmp(*this,r)<0;
    }
    bool operator<=(const pt& r) const {
        return cmp(*this,r)<=0;
    }
    bool operator>(const pt& r) const {
        return cmp(*this,r)>0;
    }
    bool operator==(const pt& r) const { return sgn((*this - r).rabs()) == 0; }
    bool operator!=(const pt& r) const { return !(*this == r); }

    ld norm() const { return x * x + y * y; }
    ld rabs() const { return max(std::abs(x), std::abs(y)); }  // robust abs
    pair<ld, ld> to_pair() const { return {x, y}; }
    #ifdef GEOF
    ld abs() const { return sqrt(norm()); }
    ld arg() const { return atan2(y, x); }
    static pt polar(ld le, ld th) { return {le * cos(th), le * sin(th)}; }
	#endif
};
istream& operator>>(istream& is, pt& p){
	return is>>p.x>>p.y;
}
ostream& operator<<(ostream& os, const pt& p) {
    return os << "pt(" << p.x << ", " << p.y << ")";
}
ld norm(const pt&a){
	return a.norm();
}
#ifdef GEOF
ld abs(const pt&a){
	return sqrt(norm(a));
}
//XXII Opencup Gpt of Ural K
pt normalized(const pt&a){
	return a/abs(a);
}
ld arg(const pt&a){return a.arg();}
//normalize to [-PI,PI)
//Contest 2: ptKU Contest 1, ptTZ Summer 2022 Day 4
ld normarg(ld a){
	ld res=fmod(a+PI,2*PI);
	if(res<0)res+=PI;
	else res-=PI;
	return res;
}
//AOJ1183
//arg between ab
//assume given lengths are valid
ld arg(ld a,ld b,ld c){
	return acos(min(max((a*a+b*b-c*c)/(2*a*b),ld(-1)),ld(1)));
}
#endif
ld norm(const pt&a,const pt&b){
	return (a-b).norm();
}
ld dot(const pt&a,const pt&b){return a.x*b.x+a.y*b.y;}
ld crs(const pt& a,const pt& b){return a.x*b.y-a.y*b.x;}
ld crs(const pt& a,const pt& b,const pt& c){return crs(b-a,c-a);}
int ccw(const pt& a,const pt& b){return sgn(crs(a,b));}
int ccw(const pt& a,const pt& b,const pt& c){return ccw(b-a,c-a);}
//(-pi,0](0,pi]
int argtype(const pt&a){
	if(sgn(a.y)==0)return a.x<0?1:0;
	return a.y<0?0:1;
}
int argcmp(const pt&a,const pt&b){
	int at=argtype(a),bt=argtype(b);
	if(at!=bt)return at<bt?-1:1;
	return -ccw(a,b);
};
bool argless(const pt&a,const pt&b){return argcmp(a,b)<0;}
//(-2)[a,-1](0)[b,1](2)
int bet(pt a,pt b,pt c){
	pt d=b-a;
	ld e=dot(d,c-a);
	if(sgn(e)<=0)return sgn(e)-1;
	return sgn(e-norm(d))+1;
}
//AOJ0153
//三角形 abc に d が含まれるか？0-no,1-edge,2-in
int cont(pt a,pt b,pt c,pt d){
	if(ccw(a,b,c)==-1) swap(b,c);
	return min({ccw(a,b,d),ccw(b,c,d),ccw(c,a,d)})+1;
}
//(a,b) を結ぶ直線を考え，x 座標との交点の y 座標を求める
//(分子,分母)を返す
pair<ld,ld> xcut(const pt&a,const pt&b,ld x){
	return mp(a.y*(b.x-x)-b.y*(a.x-x),b.x-a.x);
}
//XXII Opencup Gpt of Ural K
pt rot90(pt a){
	return pt(-a.y,a.x);
}
#ifdef GEOF
ld xcutval(const pt&a,const pt&b,ld x){
	auto [p,q]=xcut(a,b,x);
	return p/q;
}
//AOJ1183
//Xmas2010 E
//-+ の 順で返す
//a の符号により，small/large が決まる
int qeq(ld a,ld b,ld c,ld&d,ld&e){
	if(sgn(a)==0){
		if(sgn(b)==0)return 0;
		d=-c/b;
		return 1;
	}
	ld f=b*b-4*a*c;
	if(sgn(f)<0)return 0;
	ld g=sqrt(max(f,ld(0)));
	d=(-b-g)/(2*a);
	e=(-b+g)/(2*a);
	return sgn(f)+1;
}
#else
pt normdir(pt a){
	if(a==pt(0,0))return a;
	int g=gcd(a.x,a.y);
	return pt(a.x/g,a.y/g);
}
#endif

ld area2(const vc<pt>&ps){
	ld res=0;
	rep(i,si(ps))res+=crs(ps[i],ps[(i+1)%si(ps)]);
	return res;
}

//UCUP 2023-3 F
template<class F>
void segeasy(int s,int l,int r,F f){
	for(l+=s,r+=s;l<r;l>>=1,r>>=1){
		if(l&1)f(l);
		if(r&1)f(r-1);
		l++; //ceil l
	}
}

//The 1st Universal Cup. Stage 15: Hangzhou J
struct F{
	ll a,b;
	F():a(0),b(1){}
	F(ll aa,ll bb):a(aa),b(bb){}
	F(pair<ll,ll> ab):F(ab.a,ab.b){}
	static int cmp(const F&a,const F&b){
		assert(a.b>=0);
		assert(b.b>=0);
		if(a.b==0&&b.b==0){
			assert(a.a!=0);
			assert(b.a!=0);
			return int(a.a>0)-int(b.a>0);
		}
		using T=__int128;
		T c=(T)a.a*b.b;
		T d=(T)b.a*a.b;
		return c<d?-1:c==d?0:1;
	}
	F operator-()const{return F{-a,b};}
	bool operator<(const F&r)const{
		return cmp(*this,r)<0;
	}
	bool operator>(const F&r)const{
		return cmp(*this,r)>0;
	}
	bool operator>=(const F&r)const{
		return cmp(*this,r)>=0;
	}
	bool operator==(const F&r)const{
		return cmp(*this,r)==0;
	}
	bool operator!=(const F&r)const{
		return cmp(*this,r)!=0;
	}
};
const F Finf{1,0};

//max hull
//有理数で全てを計算する
//The 1st Universal Cup. Stage 15: Hangzhou J

//Author: Simon Lindholm
//https://github.com/kth-competitive-programming/kactl/blob/master/content/data-structures/LineContainer.h
struct Line {
	mutable ll a,b;
	mutable F p;
	bool operator<(const Line& o) const { return a < o.a; }
	bool operator<(F x) const { return p<x;}
};
struct LineContainer:multiset<Line,less<>>{
	F div(ll a,ll b){return b<0?F{-a,-b}:F{a,b};}
	bool isect(iterator x, iterator y) {
		if (y == end()) { x->p = Finf; return false; }
		if (x->a == y->a) x->p = x->b > y->b ? Finf : -Finf;
		else x->p = div(y->b - x->b, x->a - y->a);
		return x->p>=y->p;
	}
	void add(ll a, ll b) {
		auto z = insert({a, b, F()}), y = z++, x = y;
		while (isect(y, z)) z = erase(z);
		if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
		while ((y = x) != begin() && (--x)->p >= y->p)
			isect(x, erase(y));
	}
	//x の分母が非負でないと壊れるだろうね
	//例えば　(a,b) を add して，(pa+qb) の max を取りたい，みたいなクエリを考える
	//q>=0 ならば p/q をqueryすることで解決
	ll query(F x){
		assert(x.b>=0);
		//assert(!empty());
		if(empty())return -inf;
		auto l = *lower_bound(x);
		return l.a * x.a + l.b * x.b;
	}
};

//(x,y)->(x+y*eps,y) と変形してあると思い込む
//2 つの線分が占める x 座標の範囲に正の共通部分があるとする
//The 1st Universal Cup. Stage 15: Hangzhou J
struct S{
	//多分線分同士が端点以外で交わらないというケースだけ動くコード
	//線分に接するみたいな状況が発生すると話が変わってきてしまう
	pt a,b;
	S(){}
	S(const pt&aa,const pt&bb):a(min(aa,bb)),b(max(aa,bb)){assert(a<b);}
	bool operator<(const S&r)const{
		if(a==r.a)return ccw(a,b,r.b)>0;
		else if(a<r.a)return ccw(a,b,r.a)>0;
		else return ccw(r.a,r.b,a)<0;
	}
	F evaly(pt x)const{
		assert(a<=x&&x<=b);
		if(a.x==b.x)return F{x.y,1};
		else return xcut(a,b,x.x);
	}
	//値が 4 乗程度になりがち
	static int cmp(const S&a,const S&b,pt x){
		return F::cmp(a.evaly(x),b.evaly(x));
	}
	bool operator<(const pair<S,pt>&r)const{
		return cmp(*this,r.a,r.b)<0;
	}
};

bool dbg=false;
const int nmax=10;
const int qmax=10;
const int vmax=10;

void slv(){
	int n,q;
	if(dbg){
		n=rand_int(3,nmax);
		q=qmax;
	}else{
		cin>>n>>q;
	}
	vc<pt> ps(n);
	if(dbg){
		
	}else{
		rep(i,n)cin>>ps[i];
	}
	rotate(ps.bg,min_element(all(ps)),ps.ed);
	auto xy=ps;sort(all(xy));
	pt xymin=xy[0],xymax=xy[n-1];
	
	vc<S> qs(q);
	rep(i,q){
		pt a,b;
		if(dbg){
			do{
				a.x=rand_int(0,vmax);
				a.y=rand_int(0,vmax);
				b.x=rand_int(0,vmax);
				b.y=rand_int(0,vmax);
			}while(a==b);
		}else{
			cin>>a>>b;
		}
		qs[i]=S(a,b);
	}
	vi ans(q);
	rep(i,q){
		auto&[a,b]=qs[i];
		if(bis(xy,a)||bis(xy,b))ans[i]=1;
	}
	rep(i,q)if(ans[i]==0){
		auto [a,b]=qs[i];
		xy.pb(max(xymin,min(a,xymax)));
		xy.pb(max(xymin,min(b,xymax)));
	}
	mkuni(xy);
	int s=si(xy)-1;
	
	set<S,less<>> global;
	
	struct Q{
		F v;
		int i;
		bool operator<(const Q&r)const{
			if(v!=r.v)return v<r.v;
			else return i<r.i;
		}
	};
	vc<Q> w[2][2];
	
	auto getseg=[&](int i){
		pt a=ps[i],b=ps[(i+1)%n];
		if(a>b)swap(a,b);
		return S(a,b);
	};
	
	auto dfs=[&](auto self,int l,int r,vi pid,vi qid)->void{
		//pid の各区間は [xy[l],xy[r]] と正の交わりを持つ
		//qid の各区間は [xy[l],xy[r]] と正の交わりを持つ
		vc<decltype(global)::iterator> itrs;
		rep(i,2)rep(j,2)w[i][j].clear();
		for(int i=0;i<si(pid);){
			auto [a,b]=getseg(pid[i]);
			if(a<=xy[l]&&xy[r]<=b){
				auto [itr,ok]=global.emplace(a,b);
				itrs.pb(itr);
				assert(ok);
				i++;
			}else{
				int j=i+1;
				while(j<si(pid)){
					auto [c,d]=getseg(pid[j]);
					if(c<=xy[l]||xy[r]<=d)break;
					j++;
				}
				assert(j<si(pid));
				F lmin=Finf,lmax=-Finf;
				F rmin=Finf,rmax=-Finf;
				auto upd=[&](S t){
					if(t.a<=xy[l]){
						assert(t.b<xy[r]);
						auto v=t.evaly(xy[l]);
						chmin(lmin,v);
						chmax(lmax,v);
					}else{
						assert(xy[r]<=t.b);
						auto v=t.evaly(xy[r]);
						chmin(rmin,v);
						chmax(rmax,v);
					}
				};
				upd(getseg(pid[i]));
				upd(getseg(pid[j]));
				rng(k,i+1,j+1)w[0][0].pb({lmin,pid[k]});
				rng(k,i+1,j+1)w[0][1].pb({lmax,pid[k]});
				rng(k,i+1,j+1)w[1][0].pb({rmin,pid[k]});
				rng(k,i+1,j+1)w[1][1].pb({rmax,pid[k]});
				i=j+1;
			}
		}
		for(auto i:qid)if(ans[i]==0){
			auto [a,b]=qs[i];
			if(a<=xy[l]&&xy[r]<=b){
				auto j=global.lower_bound(mp(qs[i],xy[l]));
				if(j!=global.ed&&S::cmp(*j,qs[i],xy[l])==0){
					ans[i]=1;
					continue;
				}
				auto k=global.lower_bound(mp(qs[i],xy[r]));
				if(k!=global.ed&&S::cmp(*k,qs[i],xy[r])==0){
					ans[i]=1;
					continue;
				}
				if(j!=k){
					ans[i]=1;
				}
			}
		}
		rep(lr,2)rep(ud,2){
			for(auto i:qid)if(ans[i]==0){
				auto [a,b]=qs[i];
				if(a<=xy[l]&&xy[r]<=b){
					auto v=qs[i].evaly(lr==0?xy[l]:xy[r]);
					w[lr][ud].pb({v,inf+i});
				}
			}
			if(ud)for(auto&[v,i]:w[lr][ud])v.a=-v.a;
			sort(all(w[lr][ud]));
			LineContainer lc;
			F pre=-Finf;
			for(auto [v,i]:w[lr][ud]){
				if(i<inf){
					pt a=ps[i];
					if(ud)a.y=-a.y;
					lc.add(a.x,a.y);
					pre=v;
				}else{
					i-=inf;
					if(pre==v)ans[i]=1;
					else{
						auto [a,b]=qs[i];
						if(ud){
							a.y=-a.y;
							b.y=-b.y;
						}
						pt dir=rot90(b-a);
						ll val=lc.query(F(dir.x,dir.y));
						if(dot(a,dir)<=val)ans[i]=1;
					}
				}
			}
		}
		if(r-l>1){
			vi pl,pr,ql,qr;
			int m=(l+r)/2;
			for(auto i:pid){
				auto [a,b]=getseg(i);
				if(a<=xy[l]&&xy[r]<=b)continue;
				if(a<xy[m])pl.pb(i);
				if(xy[m]<b)pr.pb(i);
			}
			for(auto i:qid)if(ans[i]==0){
				auto [a,b]=qs[i];
				if(a<=xy[l]&&xy[r]<=b)continue;
				if(a<xy[m])ql.pb(i);
				if(xy[m]<b)qr.pb(i);
			}
			self(self,l,m,pl,ql);
			self(self,m,r,pr,qr);
		}
		for(auto itr:itrs)global.erase(itr);
	};
	dfs(dfs,0,s,vid(n),vid(q));
	if(dbg){
		
	}else{
		rep(i,q){
			if(ans[i])YES(0);
			else NO(0);
		}
	}
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	if(dbg){
	}else{
	//int t;cin>>t;rep(_,t)
		slv();
	}
}