Language: C++

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdint>
#include <cstdio>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;

using i64 = int64_t;

int R, C, N;

i64 get_ord(i64 x, i64 y) {
    if (y == 0) {
        return x;
    } else if (y == C) {
        return R + C + R - x;
    } else if (x == 0) {
        return R + C + R + C - y;
    }
    return R + y;
}

vector<pair<i64, i64> > ls, ks;

int main() {
    cin.tie(0); ios::sync_with_stdio(false);

    cin >> R >> C >> N;
    for (int j = 0; j < N; ++j) {
        i64 x1, y1, x2, y2;
        cin >> x1 >> y1 >> x2 >> y2;

        if ((x1 == 0 || x1 == R || y1 == 0 || y1 == C) &&
            (x2 == 0 || x2 == R || y2 == 0 || y2 == C)) {

            i64 o1 = get_ord(x1, y1), o2 = get_ord(x2, y2);

            ls.emplace_back(min(o1, o2), max(o1, o2));
            ks.emplace_back(max(o1, o2), min(o1, o2));
        }
    }

    sort(begin(ls), end(ls));

    for (int j = 0; j < (int)ls.size() - 1; ++j) {
        pair<i64, i64> p = *lower_bound(begin(ks), end(ks), make_pair(ls[j].second, 1LL<<60));
        i64 v1 = (ls[j].first - p.second) * (ls[j].first - p.first);
        i64 v2 = (ls[j].second - p.second) * (ls[j].second - p.first);
        if (v1 * v2 < 0) {
            cout << "NO" << endl;
            return 0;
        }
    }
    cout << "YES" << endl;


    return 0;
}


Compiler output:
In file included from /usr/include/c++/14/bits/stl_algobase.h:71,
                 from /usr/include/c++/14/algorithm:60,
                 from a.cc:1:
/usr/include/c++/14/bits/predefined_ops.h: In instantiation of 'bool __gnu_cxx::__ops::_Iter_less_val::operator()(_Iterator, _Value&) const [with _Iterator = __gnu_cxx::__normal_iterator<std::pair<long int, long int>*, std::vector<std::pair<long int, long int> > >; _Value = const std::pair<long int, long long int>]':
/usr/include/c++/14/bits/stl_algobase.h:1504:14:   required from '_ForwardIterator std::__lower_bound(_ForwardIterator, _ForwardIterator, const _Tp&, _Compare) [with _ForwardIterator = __gnu_cxx::__normal_iterator<pair<long int, long int>*, vector<pair<long int, long int> > >; _Tp = pair<long int, long long int>; _Compare = __gnu_cxx::__ops::_Iter_less_val]'
 1504 |           if (__comp(__middle, __val))
      |               ~~~~~~^~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algobase.h:1539:32:   required from '_ForwardIterator std::lower_bound(_ForwardIterator, _ForwardIterator, const _Tp&) [with _ForwardIterator = __gnu_cxx::__normal_iterator<pair<long int, long int>*, vector<pair<long int, long int> > >; _Tp = pair<long int, long long int>]'
 1539 |       return std::__lower_bound(__first, __last, __val,
      |              ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
 1540 |                                 __gnu_cxx::__ops::__iter_less_val());
      |                                 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a.cc:62:40:   required from here
   62 |         pair<i64, i64> p = *lower_bound(begin(ks), end(ks), make_pair(ls[j].second, 1LL<<60));
      |                             ~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/predefined_ops.h:69:22: error: no match for 'operator<' (operand types are 'std::pair<long int, long int>' and 'const std::pair<long int, long long int>')
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
In file included from /usr/include/c++/14/bits/stl_algobase.h:67:
/usr/include/c++/14/bits/stl_iterator.h:1241:5: note: candidate: 'template<class _IteratorL, class _IteratorR, class _Container> bool __gnu_cxx::operator<(const __normal_iterator<_IteratorL, _Container>&, const __normal_iterator<_IteratorR, _Container>&)'
 1241 |     operator<(const __normal_iterator<_IteratorL, _Container>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1241:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long int, long int>' is not derived from 'const __gnu_cxx::__normal_iterator<_IteratorL, _Container>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1249:5: note: candidate: 'template<class _Iterator, class _Container> bool __gnu_cxx::operator<(const __normal_iterator<_Iterator, _Container>&, const __normal_iterator<_Iterator, _Container>&)'
 1249 |     operator<(const __normal_iterator<_Iterator, _Container>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1249:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long int, long int>' is not derived from 'const __gnu_cxx::__normal_iterator<_Iterator, _Container>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
In file included from /usr/include/c++/14/bits/stl_algobase.h:64:
/usr/include/c++/14/bits/stl_pair.h:1045:5: note: candidate: 'template<class _T1, class _T2> constexpr bool std::operator<(const pair<_T1, _T2>&, const pair<_T1, _T2>&)'
 1045 |     operator<(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_pair.h:1045:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   deduced conflicting types for parameter '_T2' ('long int' and 'long long int')
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:448:5: note: candidate: 'template<class _Iterator> constexpr bool std::operator<(const reverse_iterator<_Iterator>&, const reverse_iterator<_Iterator>&)'
  448 |     operator<(const reverse_iterator<_Iterator>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:448:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long int, long int>' is not derived from 'const std::reverse_iterator<_Iterator>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:493:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr bool std::operator<(const reverse_iterator<_Iterator>&, const reverse_iterator<_IteratorR>&)'
  493 |     operator<(const reverse_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:493:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long int, long int>' is not derived from 'const std::reverse_iterator<_Iterator>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1694:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr bool std::operator<(const move_iterator<_IteratorL>&, const move_iterator<_IteratorR>&)'
 1694 |     operator<(const move_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1694:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long int, long int>' is not derived from 'const std::move_iterator<_IteratorL>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1760:5: note: candidate: 'template<class _Iterator> constexpr bool std::operator<(const move_iterator<_IteratorL>&, const move_iterator<_IteratorL>&)'
 1760 |     operator<(const move_iterator<_Iterator>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1760:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long int, long int>' is not derived from 'const std::move_iterator<_IteratorL>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
In file included from /usr/include/c++/14/bits/basic_string.h:47,
                 from /usr/include/c++/14/string:54,
                 from /usr/include/c++/14/bitset:52,
                 from a.cc:2:
/usr/include/c++/14/string_view:673:5: note: candidate: 'template<class _CharT, class _Traits> constexpr bool std::operator<(basic_string_view<_CharT, _Traits>, basic_string_view<_CharT, _Traits>)'
  673 |     operator< (basic_string_view<_CharT, _Traits> __x,
      |     ^~~~~~~~
/usr/include/c++/14/string_view:673:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long int, long int>' is not derived from 'std::basic_string_view<_CharT, _Traits>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/string_view:680:5: note: candidate: 'template<class _CharT, class _Traits> constexpr bool std::operator<(basic_string_view<_CharT, _Traits>, __type_identity_t<basic_string_view<_CharT, _Traits> >)'
  680 |     operator< (basic_string_view<_CharT, _Traits> __x,
      |     ^~~~~~~~
/usr/include/c++/14/string_view:680:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long int, long int>' is not derived from 'std::basic_string_view<_CharT, _Traits>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/string_view:688:5: note: candidate: 'template<class _CharT, class _Traits> constexpr bool std::operator<(__type_identity_t<basic_string_view<_CharT, _Traits> >, basic_string_view<_CharT, _Traits>)'
  688 |     operator< (__type_identity_t<basic_string_view<_CharT, _Traits>> __x,
      |     ^~~~~~~~
/usr/include/c++/14/string_view:688:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long int, long long int>' is not derived from 'std::basic_string_view<_CharT, _Traits>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/basic_string.h:3874:5: note: candidate: 'template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const __cxx11::basic_string<_CharT, _Traits, _Allocator>&, const __cxx11::basic_string<_CharT, _Traits, _Allocator>&)'
 3874 |     operator<(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/basic_string.h:3874:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long int, long int>' is not derived from 'const std::__cxx11::basic_string<_CharT, _Traits, _Allocator>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/basic_string.h:3888:5: note: candidate: 'template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const __cxx11::basic_string<_CharT, _Traits, _Allocator>&, const _CharT*)'
 3888 |     operator<(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/basic_string.h:3888:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long int, long int>' is not derived from 'const std::__cxx11::basic_string<_CharT, _Traits, _Allocator>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/basic_string.h:3901:5: note: candidate: 'template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const _CharT*, const __cxx11::basic_string<_CharT, _Traits, _Allocator>&)'
 390