#define PROBLEM "https://judge.yosupo.jp/problem/min_plus_convolution_convex_arbitrary"
//#include"../../template/template.hpp"//#include"../../misc/rng.hpp"//#include"../../dp/concave-min-plus-convolution.hpp"usingnamespaceNyaan;voidtest(){rep(_,10000){intN=rng(1,30);intM=rng(1,30);via(N),b(M);a[0]=-30;for(inti=1,d=-10;i<N;i++,d+=rng(1,10)){a[i]=a[i-1]+d;}each(x,b)x=rng(-30,30);autoc=concave_min_plus_convolution(a,b);vid(N+M-1,inf);rep(i,N)rep(j,M)amin(d[i+j],a[i]+b[j]);if(c!=d){trc(a,b);trc(c);trc(d);exit(1);}}trc2("OK");}voidq(){test();ini(N,M);via(N),b(M);in(a,b);out(concave_min_plus_convolution(a,b));}voidNyaan::solve(){intt=1;// in(t);while(t--)q();}
#line 1 "verify/verify-yosupo-math/yosupo-concave-min-plus-convolution-1.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/min_plus_convolution_convex_arbitrary"
//#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 4 "verify/verify-yosupo-math/yosupo-concave-min-plus-convolution-1.test.cpp"
//#line 2 "misc/rng.hpp"
#line 2 "internal/internal-seed.hpp"
#line 4 "internal/internal-seed.hpp"
usingnamespacestd;namespaceinternal{unsignedlonglongnon_deterministic_seed(){unsignedlonglongm=chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count();m^=9845834732710364265uLL;m^=m<<24,m^=m>>31,m^=m<<35;returnm;}unsignedlonglongdeterministic_seed(){return88172645463325252UL;}// 64 bit の seed 値を生成 (手元では seed 固定)// 連続で呼び出すと同じ値が何度も返ってくるので注意// #define RANDOMIZED_SEED するとシードがランダムになるunsignedlonglongseed(){#if defined(NyaanLocal) && !defined(RANDOMIZED_SEED)
returndeterministic_seed();#else
returnnon_deterministic_seed();#endif
}}// namespace internal#line 4 "misc/rng.hpp"
namespacemy_rand{usingi64=longlong;usingu64=unsignedlonglong;// [0, 2^64 - 1)u64rng(){staticu64_x=internal::seed();return_x^=_x<<7,_x^=_x>>9;}// [l, r]i64rng(i64l,i64r){assert(l<=r);returnl+rng()%u64(r-l+1);}// [l, r)i64randint(i64l,i64r){assert(l<r);returnl+rng()%u64(r-l);}// choose n numbers from [l, r) without overlappingvector<i64>randset(i64l,i64r,i64n){assert(l<=r&&n<=r-l);unordered_set<i64>s;for(i64i=n;i;--i){i64m=randint(l,r+1-i);if(s.find(m)!=s.end())m=r-i;s.insert(m);}vector<i64>ret;for(auto&x:s)ret.push_back(x);sort(begin(ret),end(ret));returnret;}// [0.0, 1.0)doublernd(){returnrng()*5.42101086242752217004e-20;}// [l, r)doublernd(doublel,doubler){assert(l<r);returnl+rnd()*(r-l);}template<typenameT>voidrandshf(vector<T>&v){intn=v.size();for(inti=1;i<n;i++)swap(v[i],v[randint(0,i+1)]);}}// namespace my_randusingmy_rand::randint;usingmy_rand::randset;usingmy_rand::randshf;usingmy_rand::rnd;usingmy_rand::rng;#line 6 "verify/verify-yosupo-math/yosupo-concave-min-plus-convolution-1.test.cpp"
//#line 2 "dp/concave-min-plus-convolution.hpp"
#line 4 "dp/concave-min-plus-convolution.hpp"
usingnamespacestd;#line 2 "dp/monotone-minima.hpp"
#line 5 "dp/monotone-minima.hpp"
usingnamespacestd;// NxN 行列がある// m_i := argmin_j (A_{i,j}) が単調増加であるときに m_i を列挙する// f(i, j, k) :// A[i][j] と A[i][k] を比較 (j < k が保証されている)// A[i][j] <= A[i][k] のとき true を返す関数を入れる (等号はどちらでもよい)vector<int>monotone_minima(intN,intM,constfunction<bool(int,int,int)>&f){vector<int>res(N);autodfs=[&](autorc,intis,intie,intl,intr)->void{if(is==ie)return;inti=(is+ie)/2;intm=l;for(intk=l+1;k<r;k++){if(!f(i,m,k))m=k;}res[i]=m;rc(rc,is,i,l,m+1);rc(rc,i+1,ie,m,r);};dfs(dfs,0,N,0,M);returnres;}// NxM 行列がある// m_i := argmin_j (A_{i,j}) が単調増加であるときに m_i を列挙する// A(i, j) : A[i][j] を返す関数template<typenameT>vector<int>monotone_minima(intN,intM,constfunction<T(int,int)>&A){function<bool(int,int,int)>f=[&](inti,intj,intk)->bool{returnA(i,j)<=A(i,k);};returnmonotone_minima(N,M,f);}/**
* @brief monotone minima
*/#line 7 "dp/concave-min-plus-convolution.hpp"
// a は下に凸, b は自由template<typenameT>vector<T>concave_min_plus_convolution(constvector<T>&a,constvector<T>&b){if(a.empty()orb.empty())return{};intn=a.size(),m=b.size();autoargmin=monotone_minima(n+m-1,m,[&](inti,intj,intk){if(i<k)returntrue;if(i-j>=n)returnfalse;returna[i-j]+b[j]<=a[i-k]+b[k];});vector<T>ans(n+m-1);for(inti=0;i<n+m-1;i++){intj=argmin[i];ans[i]=a[i-j]+b[j];}returnans;}// a は上に凸, b は自由template<typenameT>vector<T>concave_max_plus_convolution(constvector<T>&a,constvector<T>&b){if(a.empty()orb.empty())return{};intn=a.size(),m=b.size();autoargmin=monotone_minima(n+m-1,m,[&](inti,intj,intk){if(i<k)returntrue;if(i-j>=n)returnfalse;returna[i-j]+b[j]>=a[i-k]+b[k];});vector<T>ans(n+m-1);for(inti=0;i<n+m-1;i++){intj=argmin[i];ans[i]=a[i-j]+b[j];}returnans;}#line 8 "verify/verify-yosupo-math/yosupo-concave-min-plus-convolution-1.test.cpp"
usingnamespaceNyaan;voidtest(){rep(_,10000){intN=rng(1,30);intM=rng(1,30);via(N),b(M);a[0]=-30;for(inti=1,d=-10;i<N;i++,d+=rng(1,10)){a[i]=a[i-1]+d;}each(x,b)x=rng(-30,30);autoc=concave_min_plus_convolution(a,b);vid(N+M-1,inf);rep(i,N)rep(j,M)amin(d[i+j],a[i]+b[j]);if(c!=d){trc(a,b);trc(c);trc(d);exit(1);}}trc2("OK");}voidq(){test();ini(N,M);via(N),b(M);in(a,b);out(concave_min_plus_convolution(a,b));}voidNyaan::solve(){intt=1;// in(t);while(t--)q();}