#define PROBLEM "https://judge.yosupo.jp/problem/segment_add_get_min"
#include"../../template/template.hpp"
#include"../../segment-tree/dynamic-li-chao-tree.hpp"usingnamespaceNyaan;voidNyaan::solve(){ini(N,Q);DynamicLiChaoTree<ll,infLL>lichao(-1001001001,1001001001);rep(i,N){inl(l,r,a,b);lichao.update_line_segment(a,b,l,r-1);}rep(i,Q){inl(c);if(c==0){inl(l,r,a,b);lichao.update_line_segment(a,b,l,r-1);}else{ini(x);llans=lichao.query(x);if(ans>=infLL)out("INFINITY");elseout(ans);}}}
#line 1 "verify/verify-yosupo-ds/yosupo-dynamic-li-chao-tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/segment_add_get_min"
#line 2 "template/template.hpp"
usingnamespacestd;// intrinstic#include<immintrin.h>#include<algorithm>
#include<array>
#include<bitset>
#include<cassert>
#include<cctype>
#include<cfenv>
#include<cfloat>
#include<chrono>
#include<cinttypes>
#include<climits>
#include<cmath>
#include<complex>
#include<cstdarg>
#include<cstddef>
#include<cstdint>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<deque>
#include<fstream>
#include<functional>
#include<initializer_list>
#include<iomanip>
#include<ios>
#include<iostream>
#include<istream>
#include<iterator>
#include<limits>
#include<list>
#include<map>
#include<memory>
#include<new>
#include<numeric>
#include<ostream>
#include<queue>
#include<random>
#include<set>
#include<sstream>
#include<stack>
#include<streambuf>
#include<string>
#include<tuple>
#include<type_traits>
#include<typeinfo>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<vector>// utility#line 1 "template/util.hpp"
namespaceNyaan{usingll=longlong;usingi64=longlong;usingu64=unsignedlonglong;usingi128=__int128_t;usingu128=__uint128_t;template<typenameT>usingV=vector<T>;template<typenameT>usingVV=vector<vector<T>>;usingvi=vector<int>;usingvl=vector<longlong>;usingvd=V<double>;usingvs=V<string>;usingvvi=vector<vector<int>>;usingvvl=vector<vector<longlong>>;template<typenameT>usingminpq=priority_queue<T,vector<T>,greater<T>>;template<typenameT,typenameU>structP:pair<T,U>{template<typename...Args>P(Args...args):pair<T,U>(args...){}usingpair<T,U>::first;usingpair<T,U>::second;P&operator+=(constP&r){first+=r.first;second+=r.second;return*this;}P&operator-=(constP&r){first-=r.first;second-=r.second;return*this;}P&operator*=(constP&r){first*=r.first;second*=r.second;return*this;}template<typenameS>P&operator*=(constS&r){first*=r,second*=r;return*this;}Poperator+(constP&r)const{returnP(*this)+=r;}Poperator-(constP&r)const{returnP(*this)-=r;}Poperator*(constP&r)const{returnP(*this)*=r;}template<typenameS>Poperator*(constS&r)const{returnP(*this)*=r;}Poperator-()const{returnP{-first,-second};}};usingpl=P<ll,ll>;usingpi=P<int,int>;usingvp=V<pl>;constexprintinf=1001001001;constexprlonglonginfLL=4004004004004004004LL;template<typenameT>intsz(constT&t){returnt.size();}template<typenameT,typenameU>inlineboolamin(T&x,Uy){return(y<x)?(x=y,true):false;}template<typenameT,typenameU>inlineboolamax(T&x,Uy){return(x<y)?(x=y,true):false;}template<typenameT>inlineTMax(constvector<T>&v){return*max_element(begin(v),end(v));}template<typenameT>inlineTMin(constvector<T>&v){return*min_element(begin(v),end(v));}template<typenameT>inlinelonglongSum(constvector<T>&v){returnaccumulate(begin(v),end(v),0LL);}template<typenameT>intlb(constvector<T>&v,constT&a){returnlower_bound(begin(v),end(v),a)-begin(v);}template<typenameT>intub(constvector<T>&v,constT&a){returnupper_bound(begin(v),end(v),a)-begin(v);}constexprlonglongTEN(intn){longlongret=1,x=10;for(;n;x*=x,n>>=1)ret*=(n&1?x:1);returnret;}template<typenameT,typenameU>pair<T,U>mkp(constT&t,constU&u){returnmake_pair(t,u);}template<typenameT>vector<T>mkrui(constvector<T>&v,boolrev=false){vector<T>ret(v.size()+1);if(rev){for(inti=int(v.size())-1;i>=0;i--)ret[i]=v[i]+ret[i+1];}else{for(inti=0;i<int(v.size());i++)ret[i+1]=ret[i]+v[i];}returnret;};template<typenameT>vector<T>mkuni(constvector<T>&v){vector<T>ret(v);sort(ret.begin(),ret.end());ret.erase(unique(ret.begin(),ret.end()),ret.end());returnret;}template<typenameF>vector<int>mkord(intN,Ff){vector<int>ord(N);iota(begin(ord),end(ord),0);sort(begin(ord),end(ord),f);returnord;}template<typenameT>vector<int>mkinv(vector<T>&v){intmax_val=*max_element(begin(v),end(v));vector<int>inv(max_val+1,-1);for(inti=0;i<(int)v.size();i++)inv[v[i]]=i;returninv;}vector<int>mkiota(intn){vector<int>ret(n);iota(begin(ret),end(ret),0);returnret;}template<typenameT>Tmkrev(constT&v){Tw{v};reverse(begin(w),end(w));returnw;}template<typenameT>boolnxp(T&v){returnnext_permutation(begin(v),end(v));}// 返り値の型は入力の T に依存// i 要素目 : [0, a[i])template<typenameT>vector<vector<T>>product(constvector<T>&a){vector<vector<T>>ret;vector<T>v;autodfs=[&](autorc,inti)->void{if(i==(int)a.size()){ret.push_back(v);return;}for(intj=0;j<a[i];j++)v.push_back(j),rc(rc,i+1),v.pop_back();};dfs(dfs,0);returnret;}// F : function(void(T&)), mod を取る操作// T : 整数型のときはオーバーフローに注意するtemplate<typenameT>TPower(Ta,longlongn,constT&I,constfunction<void(T&)>&f){Tres=I;for(;n;f(a=a*a),n>>=1){if(n&1)f(res=res*a);}returnres;}// T : 整数型のときはオーバーフローに注意するtemplate<typenameT>TPower(Ta,longlongn,constT&I=T{1}){returnPower(a,n,I,function<void(T&)>{[](T&)->void{}});}template<typenameT>TRev(constT&v){Tres=v;reverse(begin(res),end(res));returnres;}template<typenameT>vector<T>Transpose(constvector<T>&v){usingU=typenameT::value_type;if(v.empty())return{};intH=v.size(),W=v[0].size();vectorres(W,T(H,U{}));for(inti=0;i<H;i++){for(intj=0;j<W;j++){res[j][i]=v[i][j];}}returnres;}template<typenameT>vector<T>Rotate(constvector<T>&v,intclockwise=true){usingU=typenameT::value_type;intH=v.size(),W=v[0].size();vectorres(W,T(H,U{}));for(inti=0;i<H;i++){for(intj=0;j<W;j++){if(clockwise){res[W-1-j][i]=v[i][j];}else{res[j][H-1-i]=v[i][j];}}}returnres;}}// namespace Nyaan#line 58 "template/template.hpp"
// bit operation#line 1 "template/bitop.hpp"
namespaceNyaan{__attribute__((target("popcnt")))inlineintpopcnt(constu64&a){return__builtin_popcountll(a);}inlineintlsb(constu64&a){returna?__builtin_ctzll(a):64;}inlineintctz(constu64&a){returna?__builtin_ctzll(a):64;}inlineintmsb(constu64&a){returna?63-__builtin_clzll(a):-1;}template<typenameT>inlineintgbit(constT&a,inti){return(a>>i)&1;}template<typenameT>inlinevoidsbit(T&a,inti,boolb){if(gbit(a,i)!=b)a^=T(1)<<i;}constexprlonglongPW(intn){return1LL<<n;}constexprlonglongMSK(intn){return(1LL<<n)-1;}}// namespace Nyaan#line 61 "template/template.hpp"
// inout#line 1 "template/inout.hpp"
namespaceNyaan{template<typenameT,typenameU>ostream&operator<<(ostream&os,constpair<T,U>&p){os<<p.first<<" "<<p.second;returnos;}template<typenameT,typenameU>istream&operator>>(istream&is,pair<T,U>&p){is>>p.first>>p.second;returnis;}template<typenameT>ostream&operator<<(ostream&os,constvector<T>&v){ints=(int)v.size();for(inti=0;i<s;i++)os<<(i?" ":"")<<v[i];returnos;}template<typenameT>istream&operator>>(istream&is,vector<T>&v){for(auto&x:v)is>>x;returnis;}istream&operator>>(istream&is,__int128_t&x){stringS;is>>S;x=0;intflag=0;for(auto&c:S){if(c=='-'){flag=true;continue;}x*=10;x+=c-'0';}if(flag)x=-x;returnis;}istream&operator>>(istream&is,__uint128_t&x){stringS;is>>S;x=0;for(auto&c:S){x*=10;x+=c-'0';}returnis;}ostream&operator<<(ostream&os,__int128_tx){if(x==0)returnos<<0;if(x<0)os<<'-',x=-x;stringS;while(x)S.push_back('0'+x%10),x/=10;reverse(begin(S),end(S));returnos<<S;}ostream&operator<<(ostream&os,__uint128_tx){if(x==0)returnos<<0;stringS;while(x)S.push_back('0'+x%10),x/=10;reverse(begin(S),end(S));returnos<<S;}voidin(){}template<typenameT,class...U>voidin(T&t,U&...u){cin>>t;in(u...);}voidout(){cout<<"\n";}template<typenameT,class...U,charsep=' '>voidout(constT&t,constU&...u){cout<<t;if(sizeof...(u))cout<<sep;out(u...);}structIoSetupNya{IoSetupNya(){cin.tie(nullptr);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);cerr<<fixed<<setprecision(7);}}iosetupnya;}// namespace Nyaan#line 64 "template/template.hpp"
// debug#line 1 "template/debug.hpp"
namespaceDebugImpl{template<typenameU,typename=void>structis_specialize:false_type{};template<typenameU>structis_specialize<U,typenameconditional<false,typenameU::iterator,void>::type>:true_type{};template<typenameU>structis_specialize<U,typenameconditional<false,decltype(U::first),void>::type>:true_type{};template<typenameU>structis_specialize<U,enable_if_t<is_integral<U>::value,void>>:true_type{};voiddump(constchar&t){cerr<<t;}voiddump(conststring&t){cerr<<t;}voiddump(constbool&t){cerr<<(t?"true":"false");}voiddump(__int128_tt){if(t==0)cerr<<0;if(t<0)cerr<<'-',t=-t;stringS;while(t)S.push_back('0'+t%10),t/=10;reverse(begin(S),end(S));cerr<<S;}voiddump(__uint128_tt){if(t==0)cerr<<0;stringS;while(t)S.push_back('0'+t%10),t/=10;reverse(begin(S),end(S));cerr<<S;}template<typenameU,enable_if_t<!is_specialize<U>::value,nullptr_t>=nullptr>voiddump(constU&t){cerr<<t;}template<typenameT>voiddump(constT&t,enable_if_t<is_integral<T>::value>*=nullptr){stringres;if(t==Nyaan::inf)res="inf";ifconstexpr(is_signed<T>::value){if(t==-Nyaan::inf)res="-inf";}ifconstexpr(sizeof(T)==8){if(t==Nyaan::infLL)res="inf";ifconstexpr(is_signed<T>::value){if(t==-Nyaan::infLL)res="-inf";}}if(res.empty())res=to_string(t);cerr<<res;}template<typenameT,typenameU>voiddump(constpair<T,U>&);template<typenameT>voiddump(constpair<T*,int>&);template<typenameT>voiddump(constT&t,enable_if_t<!is_void<typenameT::iterator>::value>*=nullptr){cerr<<"[ ";for(autoit=t.begin();it!=t.end();){dump(*it);cerr<<(++it==t.end()?"":", ");}cerr<<" ]";}template<typenameT,typenameU>voiddump(constpair<T,U>&t){cerr<<"( ";dump(t.first);cerr<<", ";dump(t.second);cerr<<" )";}template<typenameT>voiddump(constpair<T*,int>&t){cerr<<"[ ";for(inti=0;i<t.second;i++){dump(t.first[i]);cerr<<(i==t.second-1?"":", ");}cerr<<" ]";}voidtrace(){cerr<<endl;}template<typenameHead,typename...Tail>voidtrace(Head&&head,Tail&&...tail){cerr<<" ";dump(head);if(sizeof...(tail)!=0)cerr<<",";trace(std::forward<Tail>(tail)...);}}// namespace DebugImpl#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"
// macro#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
#line 70 "template/template.hpp"
namespaceNyaan{voidsolve();}intmain(){Nyaan::solve();}#line 2 "segment-tree/dynamic-li-chao-tree.hpp"
#line 2 "data-structure/hash-map-variable-length.hpp"
template<typenameKey,typenameVal>structHashMap{usingu32=uint32_t;usingu64=uint64_t;u32cap,s;vector<Key>keys;vector<Val>vals;vector<bool>flag;u64r;u32shift;ValDefaultValue;staticu64rng(){u64m=chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count();m^=m>>16;m^=m<<32;returnm;}voidreallocate(){cap<<=1;vector<Key>k(cap);vector<Val>v(cap);vector<bool>f(cap);u32sh=shift-1;for(inti=0;i<(int)flag.size();i++){if(flag[i]){u32hash=(u64(keys[i])*r)>>sh;while(f[hash])hash=(hash+1)&(cap-1);k[hash]=keys[i];v[hash]=vals[i];f[hash]=1;}}keys.swap(k);vals.swap(v);flag.swap(f);--shift;}explicitHashMap():cap(8),s(0),keys(cap),vals(cap),flag(cap),r(rng()),shift(64-__lg(cap)),DefaultValue(Val()){}Val&operator[](constKey&i){u32hash=(u64(i)*r)>>shift;while(true){if(!flag[hash]){if(s+s/4>=cap){reallocate();return(*this)[i];}keys[hash]=i;flag[hash]=1;++s;returnvals[hash]=DefaultValue;}if(keys[hash]==i)returnvals[hash];hash=(hash+1)&(cap-1);}}// exist -> return pointer of Val// not exist -> return nullptrconstVal*find(constKey&i)const{u32hash=(u64(i)*r)>>shift;while(true){if(!flag[hash])returnnullptr;if(keys[hash]==i)return&(vals[hash]);hash=(hash+1)&(cap-1);}}// return vector< pair<const Key&, val& > >vector<pair<Key,Val>>enumerate()const{vector<pair<Key,Val>>ret;for(u32i=0;i<cap;++i)if(flag[i])ret.emplace_back(keys[i],vals[i]);returnret;}intsize()const{returns;}// set default_valuevoidset_default(constVal&val){DefaultValue=val;}};/**
* @brief Hash Map(可変長版)
* @docs docs/data-structure/hash-map.md
*/#line 6 "segment-tree/dynamic-li-chao-tree.hpp"
template<typenameT,TINF>structDynamicLiChaoTree{structLine{Tslope,intercept;Line():slope(0),intercept(INF){}Line(Tslope,Tintercept):slope(slope),intercept(intercept){}inlineTget(Tx)const{returnslope*x+intercept;}inlineboolover(constLine&other,constT&x)const{returnget(x)<other.get(x);}};// remind セグ木は1-indexedの実装Txmin,xmax,_size;HashMap<T,Line>seg;// [l , r]におけるLi Chao TreeDynamicLiChaoTree(Txmin,Txmax):xmin(xmin),xmax(xmax){_size=1;while(_size<xmax-xmin+1)_size<<=1;}private:// 内部用の関数voidupdate(Ta,Tb,Tleft,Tright,Tseg_idx){Lineline(a,b);while(1){Tmid=(left+right)>>1;booll_over=line.over(seg[seg_idx],min(xmax,left+xmin));boolr_over=line.over(seg[seg_idx],min(xmax,right-1+xmin));if(l_over==r_over){if(l_over)swap(seg[seg_idx],line);return;}boolm_over=line.over(seg[seg_idx],min(xmax,mid+xmin));if(m_over)swap(seg[seg_idx],line);if(l_over!=m_over)seg_idx=(seg_idx<<1),right=mid;elseseg_idx=(seg_idx<<1)|1,left=mid;}}// 内部用の関数voidupdate(Ta,Tb,Tseg_idx){Tleft,right;Tupper_bit=63-__builtin_clzll(seg_idx);left=(_size>>upper_bit)*(seg_idx-(1<<upper_bit));right=left+(_size>>upper_bit);update(a,b,left,right,seg_idx);}public:// y = ax + bなる直線を追加voidupdate(Ta,Tb){update(a,b,0,_size,1);}// 閉区間x in [left , right]に線分y = ax + bを追加するクエリvoidupdate_line_segment(Ta,Tb,Tleft,Tright){left-=xmin-_size,right-=xmin-_size-1;for(;left<right;left>>=1,right>>=1){if(left&1)update(a,b,left++);if(right&1)update(a,b,--right);}}// xにおける最小値クエリTquery(Tx){Tleft=0,right=_size,seg_idx=1,idx=x-xmin,ret=INF;while(1){Tcur=seg[seg_idx].get(x);// 線分追加クエリがない場合はここのコメントアウトを外して高速化可能(1.5倍程度?)// if(cur == INF) break;ret=min(ret,cur);if(left+1>=right)break;Tmid=(left+right)>>1;if(idx<mid)seg_idx=(seg_idx<<1),right=mid;elseseg_idx=(seg_idx<<1)|1,left=mid;}returnret;}};#line 5 "verify/verify-yosupo-ds/yosupo-dynamic-li-chao-tree.test.cpp"
usingnamespaceNyaan;voidNyaan::solve(){ini(N,Q);DynamicLiChaoTree<ll,infLL>lichao(-1001001001,1001001001);rep(i,N){inl(l,r,a,b);lichao.update_line_segment(a,b,l,r-1);}rep(i,Q){inl(c);if(c==0){inl(l,r,a,b);lichao.update_line_segment(a,b,l,r-1);}else{ini(x);llans=lichao.query(x);if(ans>=infLL)out("INFINITY");elseout(ans);}}}