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

template<class t>
vc<t> presum(const vc<t>&a){
	vc<t> s(si(a)+1);
	rep(i,si(a))s[i+1]=s[i]+a[i];
	return s;
}
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,size_t K,class s=t>
s SUM(const array<t,K>&a){
	return accumulate(all(a),s(0));
}

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

template<class t>
pair<t,int> MAXi(const vc<t>&a){
	auto itr=max_element(all(a));
	return mp(*itr,itr-a.bg);
}

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

template<class t>
pair<t,int> MINi(const vc<t>&a){
	auto itr=min_element(all(a));
	return mp(*itr,itr-a.bg);
}

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

template<class S>
void soin(S&s){
	sort(all(s));
}

template<class S,class F>
void soin(S&s,F&&f){
	sort(all(s),forward<F>(f));
}

template<class S>
S soout(S s){
	soin(s);
	return s;
}

template<class S>
void rein(S&s){
	reverse(all(s));
}

template<class S>
S reout(S s){
	rein(s);
	return s;
}

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

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

template<class t,class u>
void pb(vc<t>&a,const vc<u>&b){
	a.insert(a.ed,all(b));
}

template<class t,class...Args>
vc<t> cat(vc<t> a,Args&&...b){
	(pb(a,forward<Args>(b)),...);
	return a;
}

template<class t,class u>
vc<t>& operator+=(vc<t>&a,u x){
	for(auto&v:a)v+=x;
	return a;
}

template<class t,class u>
vc<t> operator+(vc<t> a,u x){
	return a+=x;
}

template<class t>
vc<t> operator+(const vc<t>&a,const vc<t>&b){
	vc<t> c(max(si(a),si(b)));
	rep(i,si(a))c[i]+=a[i];
	rep(i,si(b))c[i]+=b[i];
	return c;
}

template<class t,class u>
vc<t>& operator-=(vc<t>&a,u x){
	for(auto&v:a)v-=x;
	return a;
}

template<class t,class u>
vc<t>& operator-(vc<t> a,u x){
	return a-=x;
}

template<class t,class u>
void remval(vc<t>&a,const u&v){
	a.erase(remove(all(a),v),a.ed);
}
//消した要素の個数を返してくれる
//UCUP 2-8-F
template<class t,class F>
int remif(vc<t>&a,F f){
	auto itr=remove_if(all(a),f);
	int res=a.ed-itr;
	a.erase(itr,a.ed);
	return res;
}

template<class VS,class u>
void fila(VS&vs,const u&a){
	fill(all(vs),a);
}

template<class t,class u>
int findid(const vc<t>&vs,const u&a){
	auto itr=find(all(vs),a);
	if(itr==vs.ed)return -1;
	else return itr-vs.bg;
}

template<class t>
void rtt(vc<t>&vs,int i){
	rotate(vs.bg,vs.bg+i,vs.ed);
}

//copied from yosupo's library
//PARTLY 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();
}
ld rabs(const pt&a){
	return a.rabs();
}
#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;
}
//normalize to [0,2*PI)
//Multiuni2023-10-E
ld normarg_nonnegative(ld a){
	ld res=fmod(a,2*PI);
	if(res<0)res+=2*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;
}



using ln=pair<pt,pt>;
pt dir(ln a){return a.b-a.a;}
pt eval(ln a,ld b){return a.a+dir(a)*b;}
ld crs(ln a,pt b){return crs(a.a,a.b,b);}
int ccw(ln a,pt b){return ccw(a.a,a.b,b);}
int bet(ln a,pt b){return bet(a.a,a.b,b);}
ld projt(ln a,pt b){
	pt c=dir(a);
	return dot(c,b-a.a)/norm(c);
}
pt proj(ln a,pt b){
	pt c=dir(a);
	return a.a+c*dot(c,b-a.a)/norm(c);
}
pt refl(ln a,pt b){
	return proj(a,b)*2-b;
}
//AOJ1157
//0-no,1-yes(endpoint),2-yes(innner),3-overelap
//if the two line touch like this
// x----x----x
//it returns 1
int iss(ln a,ln b){
	int c1=ccw(a.a,a.b,b.a),c2=ccw(a.a,a.b,b.b);
	int d1=ccw(b.a,b.b,a.a),d2=ccw(b.a,b.b,a.b);
	if(c1||c2||d1||d2)return 1-max(c1*c2,d1*d2);
	int f=bet(a.a,a.b,b.a),g=bet(a.a,a.b,b.b);
	if(max(f,g)==-2||min(f,g)==2)return 0;
	if(max(f,g)==-1||min(f,g)==1)return 1;
	return 3;
}
//segment a intersects line b?
//endpoints inclusive
bool isl(ln a,ln b){
	int d1=ccw(b.a,b.b,a.a),d2=ccw(b.a,b.b,a.b);
	return d1*d2<=0;
}
//並行でない->true, というだけ
//直線が一致とかは考えてないことに注意
bool ill(ln a,ln b){
	return ccw(dir(a),dir(b));
}
ld cllt(ln a,ln b){
	return crs(b.a,b.b,a.a)/crs(dir(a),dir(b));
}
//ICPC Yokohama 2022 J
pair<ld,ld> clltf(ln a,ln b){
	return mp(crs(b.a,b.b,a.a),crs(dir(a),dir(b)));
}
//AOJ1033
pt cll(ln a,ln b){
	return eval(a,crs(b.a,b.b,a.a)/crs(dir(a),dir(b)));
}
#ifdef GEOF
//AOJ2201
ld dlp(ln a,pt b){
	return abs(crs(a,b)/abs(dir(a)));
}
//AOJ0153
ld dsp(ln a,pt b){
	pt c=proj(a,b);
	if(abs(bet(a.a,a.b,c))<=1)return abs(b-c);
	return min(abs(b-a.a),abs(b-a.b));
}
//ABC314H
//b から最も近い a 上の点を返す
pt dsp_tar(ln a,pt b){
	pt c=proj(a,b);
	if(abs(bet(a.a,a.b,c))<=1)return c;
	return abs(b-a.a)<abs(b-a.b)?a.a:a.b;
}
//AOJ1157
ld dss(ln a,ln b){
	if(iss(a,b))return 0;
	return min({dsp(a,b.a),dsp(a,b.b),dsp(b,a.a),dsp(b,a.b)});
}
//AOJ2160
//反時計回り方向に伸びる垂直二等分線
ln vbis(pt a,pt b){
	pt c=(a+b)*ld(0.5),d=b-a;
	return ln(c,pt(c.x-d.y,c.y+d.x));
}
ld cutareat(ln z,ld l,ld r){
	pt a=eval(z,l);
	pt b=eval(z,r);
	return -(b.x-a.x)*(a.y+b.y)/2;
}
#endif
//ABC286H
//simple polygon と線分が交わるか
//接している場合も true
/*
bool icl(const vc<pt>&ps,ln z){
	int n=si(ps);
	rep(i,n){
		pt p=ps[i],q=ps[(i+1)%n];
		if(iss(z,ln(p,q)))return true;
	}
	return cont(ps,z.a);
}*/

//f(x) が ] -1 | 0 | 1 [ みたいな形をしているとする
//f(0)<=0 を仮定
//f(inf)=1 を仮定
//f(x)=0 なる x を見つけてくる．
//分母最小，その中で分子最小を見つける
//f(x)=0 なる call の中で最後のやつが答えになっている
//stress-tested
template<class F>
pi frac_bisect(F func){
	pi lw(0,1),up(1,0);
	int f;
	auto load=[&](pi v){
		f=func(v);
		assert(inc(-1,f,1));
	};
	load(lw);
	assert(f<=0);
	if(f==0)return lw;
	auto mid=[&](int a,int b){
		return pi(lw.a*a+up.a*b,lw.b*a+up.b*b);
	};
	load(mid(1,1));
	while(1){
		//func(lw)==-1
		//func(up)==1
		if(f==0)return mid(1,1);
		else if(f==-1){
			int w=1;
			while(1){
				w*=2;
				load(mid(1,w));
				if(f>-1)break;
			}
			int l=w/2,r=w,rf=f;
			while(r-l>1){
				const int v=(l+r)/2;
				load(mid(1,v));
				if(f==-1)l=v;
				else{
					r=v;
					rf=f;
				}
			}
			lw=mid(1,l);
			f=rf;
		}else if(f==1){
			int w=1;
			while(1){
				w*=2;
				load(mid(w,1));
				if(f<1)break;
			}
			int l=w/2,r=w,rf=f;
			while(r-l>1){
				const int v=(l+r)/2;
				load(mid(v,1));
				if(f==1)l=v;
				else{
					r=v;
					rf=f;
				}
			}
			up=mid(l,1);
			f=rf;
		}else assert(0);
	}
}

bool dbg=false;

//デバッグ実行でオーバーフローするとコアダンプしがち

using int128=__int128_t;
using uint128=unsigned __int128_t;

istream& operator>>(istream&is,int128&res){
	res=0;
	string s;is>>s;
	int head=0;
	int128 w=1;
	if(s[0]=='-'){
		w=-1;
		head++;
	}
	while(head<int(s.size())){
		res=res*10+s[head++]-'0';
	}
	res*=w;
	return is;
}
ostream& operator<<(ostream&os,int128 i){
	if(i==0)
		return os<<0;
	static char buf[100];
	if(i<0){
		os<<"-";
		i=-i;
	}
	int p=0;
	while(i){
		buf[p++]='0'+i%10;
		i/=10;
	}
	reverse(buf,buf+p);
	buf[p]=0;
	return os<<buf;
}
ostream& operator<<(ostream&os,uint128 i){
	if(i==0)
		return os<<0;
	static char buf[100];
	int p=0;
	while(i){
		buf[p++]='0'+i%10;
		i/=10;
	}
	reverse(buf,buf+p);
	buf[p]=0;
	return os<<buf;
}
int128 abs128(int128 a){
	return a<0?-a:a;
}
int botbit(int128 a){
	const int128 m=(int128(1)<<64)-1;
	if(a&m)return __builtin_ctzll(ll(a));
	else return __builtin_ctzll(ll(a>>64))+64;
}
int128 gcd(int128 a,int128 b){
	if(a<0)a=-a;
	if(b<0)b=-b;
	if(a==0)return b;
	if(b==0)return a;
	int128 s=botbit(a|b);
	a>>=botbit(a);
	do{
		b>>=botbit(b);
		if(a>b)swap(a,b);
		b-=a;
	}while(b);
	return a<<s;
}
const int128 inf128=int128(1)<<122;
//UCUP 2-Prime-97
int128 fld(int128 a,int128 b) { // floored division
	return a / b - ((a ^ b) < 0 && a % b); }
int128 cld(int128 a, int128 b) { // ceiled division
	return a / b + ((a ^ b) > 0 && a % b); }
//a,c O(10^36)
//b,d O(10^18)
//a/b, c/d の大小比較
int cmpfrac(int128 a,int128 b,int128 c,int128 d){
	assert(b);
	assert(d);
	if(b<0){
		a=-a;
		b=-b;
	}
	if(d<0){
		c=-c;
		d=-d;
	}
	int128 x=fld(a,b),y=fld(c,d);
	if(x<y)return -1;
	if(x>y)return 1;
	int128 u=(a-x*b)*d,v=(c-y*d)*b;
	if(u<v)return -1;
	if(u>v)return 1;
	return 0;
}
bool inc(int128 a,int128 b,int128 c){
	return a<=b&&b<=c;
}

//CF530E,ARC055D
//yosupo sum_of_floor_of_linear
//x_i=floor((a*i+b)/c), i=0,1,..n-1
//c>0
//UCUP 2-Prime-43
//n>=0, n,a,c が O(10^9) で b が O(10^18)
int gauss_sum(int n,int a,int b,int c){
	if(n==0)return 0;
	int res=0;
	{
		int p=fld(a,c);
		res+=n*(n-1)/2*p;
		a-=p*c;
	}
	{
		int p=fld(b,c);
		res+=n*p;
		b-=p*c;
	}
	if(a==0)return res;
	int top=(a*(n-1)+b)/c;
	res+=top*n;
	int h=(b+1+c-1)/c;
	if(h<=top)
		res-=gauss_sum(top-h+1,c,c*h-(b+1),a)+top-h+1;
	return res;
}

//Not Verified (9割くらい大丈夫だと思うけど)
//c>=0: Prime New Year Contest 2022 7
//UCUP 2-prime-43
//↑ l,r,a,c が O(10^9) で b が O(10^18)
int gauss_helper(int l,int r,int a,int b,int c){
	int s=1;
	if(r<l){
		s=-s;
		swap(l,r);
	}
	if(c<0){
		a=-a;
		b=-b;
		c=-c;
	}
	b+=l*a;
	return gauss_sum(r-l,a,b,c)*s;
}

//x+=y*eps した座標系で考える
//直線 w を伸ばしてその下にある格子点の数を数える
//[eval(w,0),eval(w,p/q)) と進むことを考える．
//y 座標正の点を + の点，非正の点を - の点と呼ぶことにする．
//strict below にある + と weak above にある - を足し合わせる．
//これが result.a
//result.b は直線上の点の個数
//w が左向きだった場合は -1 倍される
//w=O(10^9), p,q=O(10^18)
pi sub(ln w,int p,int q){
	//dmp2(w,p,q);
	
	bool sw=w.a>w.b;
	if(sw)w=mp(-w.a+pt(0,1),-w.b+pt(0,1));
	int t=0;
	
	pt d=dir(w);
	{
		int g=gcd(d.x,d.y);
		int h=gcd(q,g);
		q/=h;
		p*=g/h;
		d/=g;
	}
	//dmp(d);
	int online=cld(p,q);
	if(0<d.x){
		int l=1,r=fld((int128)d.x*p,q);
		if(w.a.y>0)t++;
		else t+=w.a.y;
		int v=fld((int128)r*d.y,d.x)+w.a.y;
		if(p%q==0){
			if(v>0)t+=v-1;
		}else if((int128)d.x*p%q==0){
			if(v>0)t+=v;
		}else{
			t+=v;
		}
		//dmp2(l,r,below);
		//dmp2(l,r,d.y,d.x*w.a.y,d.x);
		t+=gauss_helper(l,r,d.y,d.x*w.a.y,d.x);
		//dmp(below);
		t-=online;
	}else{
		t=max<ll>(1-(w.a.y+online),0)-max<ll>(1-w.a.y,0);
	}
	
	if(sw){
		t+=online;
		online*=-1;
	}
	
	//dmp2(t,online);
	
	return pi(t,online);
}

int adjust(pt in,pt out){
	int c=ccw(in,out);
	if(in<pt()&&pt()<out&&c==1)
		return 1;
	if(out<pt()&&pt()<in&&c==-1)
		return -1;
	return 0;
}

//int128!! (for cmpfrac)
//simple polygon と直線が与えられる
//simple polygon (周含む) と直線の交わる区間を列挙する
vc<pi> overlap_ranges(const vc<pt>&ps,ln z){
	const int n=si(ps);
	vc<pi> res;
	rep(i,n){
		pt p=ps[i],q=ps[(i+1)%n],r=ps[(i+n-1)%n];
		int a=ccw(z,p),b=ccw(z,q);
		if(a*b==-1){
			res.pb(clltf(z,ln(p,q)));
		}
		if(a==0){
			pi u(rabs(ps[i]-z.a),rabs(dir(z)));
			int c=ccw(z,r);
			if(b!=c&&(b*c<0||ccw(p,q,r)>0))
				res.pb(u);
			if(b*c==1&&ccw(p,q,r)>0){
				res.pb(u);
				res.pb(u);
			}
		}
	}
	assert(si(res)%2==0);
	soin(res,[&](pi a,pi b){
		return cmpfrac(a.a,a.b,b.a,b.b)<0;
	});
	return res;
}

void slv(){
	int n,k;cin>>n>>k;
	k--;
	
	vc<pt> ps(n);
	rep(i,n)cin>>ps[i];
	
	pt ans;
	
	auto work=[&](pi tilt)->int{
		//dmp(tilt);
		//if(max(abs(tilt.b),abs(tilt.a))>2)exit(0);
		pt K(tilt.b,tilt.a);
		vi ct(n);
		rep(i,n)ct[i]=ccw(K,ps[i]);
		vc<bool> use(n);
		rep(i,n){
			if(ct[i]<=0){
				use[i]=true;
			}else{
				use[i]=false;
			}
		}
		//dmp(use);
		
		//vc<tuple<int128,int128,int128>> fs;
		vc<pi> ts;
		
		int tot=0,asum=0;
		
		rep(i,n){
			int j=(i+1)%n;
			ln w(ps[i],ps[j]);
			if(use[i]){
				asum+=adjust(ps[i]-ps[(i+n-1)%n],ps[j]-ps[i]);
				
				int p=1,q=1;
				if(!use[j]){
					tie(p,q)=clltf(w,ln(pt(),-K));//18,18
					ts.pb(clltf(ln(pt(),-K),ln(ps[i],ps[j])));
					
					{
						auto [u,v]=ts.back();
						if(u%v==0)
							asum+=adjust(ps[j]-ps[i],-K);
					}
				}
				auto [va,vb]=sub(w,p,q);
				if(ps[i]<ps[j]){//-
					tot-=va;
				}else{//+
					tot-=va+vb;
				}
			}else if(use[j]){
				auto [p,q]=clltf(w,ln(pt(),-K));//18,18
				ts.pb(clltf(ln(pt(),-K),ln(ps[i],ps[j])));
				
				{
					auto [u,v]=ts.back();
					if(u%v==0)
						asum+=adjust(-K,ps[j]-ps[i]);
				}
				
				auto [va,vb]=sub(w,1,1);
				auto [wa,wb]=sub(w,p,q);
				if(ps[i]<ps[j]){//-
					tot-=va-wa;
				}else{//+
					tot-=(va-wa)+(vb-wb);
				}
			}
		}
		
		soin(ts,[&](pi a,pi b){
			return cmpfrac(a.a,a.b,b.a,b.b)<0;
		});
		
		//dmp(ts);
		
		assert(si(ts)%2==0);
		
		rep(i,si(ts)){
			auto [va,vb]=sub(ln(pt(),-K),ts[i].a,ts[i].b);
			if(i%2==0)tot+=va+vb;
			else tot-=va+vb;
		}
		
		vc<pi> os=overlap_ranges(ps,ln(pt(),K));
		//dmp(os);
		
		int online=0;
		for(int i=0;i<si(os);i+=2){
			int l=cld(os[i].a,os[i].b);
			int r=cld(os[i+1].a+1,os[i+1].b);
			online+=r-l;
		}
		
		tot+=asum;
		//dmp2(tot,asum,online);
		if(inc(tot-online,k,tot-1)){
			int need=k-(tot-online);
			assert(need>=0);
			for(int i=0;i<si(os);i+=2){
				int l=cld(os[i].a,os[i].b);
				int r=cld(os[i+1].a+1,os[i+1].b);
				int u=(r-l);
				if(need<u){
					ans=K*(l+need);
					need-=u;
					break;
				}else{
					need-=u;
				}
			}
			assert(need<0);
			return 0;
		}
		//if(tilt==pi(1,2))exit(0);
		assert(tot>=0);
		if(tot<=k)return -1;
		if(k<tot-online)return 1;
		assert(false);
	};
	
	frac_bisect(work);
	
	print(ans.x,ans.y);
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	if(dbg){
		while(1)slv();
	}else{
		int t;cin>>t;rep(_,t)
		slv();
	}
}