Language: C++

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

typedef long long ll;
const ll maxn = 2e5+100;
ll N,X,D;

struct SECTION {
    ll l,r;
    SECTION() {}
    SECTION(int l,int r):l(l),r(r) {}
    bool operator<(const SECTION& oth) {
        if(oth.l == l) return r < oth.r;
        return l < oth.l;
    }
};
map<ll,int> idx;
vector<SECTION> sec[maxn];

int main() {
    ll key,base,cnt;
    ll L,R,ans = 0;
    ios::sync_with_stdio(false);
    cin >> N >> X >> D;
    if(!D) {
        cout << N+1 << endl;
        return 0;
    }
    cnt = 0;
    for(int k=0; k<=N; k++) {
        base = k*D+X;
        key = base%D;
        base /= D;
        if(!idx[key]) idx[key] = ++cnt;
        L = R = D;
        L += (k-1)*k/2;
        R += (2*N-k-1)*k/2;
        sec[idx[key]].push_back({--L,R});
    }
    for(int i=1; i<=cnt; i++) {
        sort(sec[i].begin(),sec[i].end());
        SECTION per = sec[i];
        for(SECTION now: sec[i]) {
            if(now.l > per.r) {
                ans += per.r - per.l;
                per = now;
            } else {
                per.r = max(per.r,now.r);
            }

            if(now == sec[i].back()) {
                ans += per.r - per.l;
            }
        }
    }
    cout << ans << endl;
    return 0;
}

Compiler output:
a.cc: In function 'int main()':
a.cc:38:34: warning: narrowing conversion of '-- L' from 'll' {aka 'long long int'} to 'int' [-Wnarrowing]
   38 |         sec[idx[key]].push_back({--L,R});
      |                                  ^~~
a.cc:38:38: warning: narrowing conversion of 'R' from 'll' {aka 'long long int'} to 'int' [-Wnarrowing]
   38 |         sec[idx[key]].push_back({--L,R});
      |                                      ^
a.cc:42:28: error: conversion from 'std::vector<SECTION>' to non-scalar type 'SECTION' requested
   42 |         SECTION per = sec[i];
      |                       ~~~~~^
a.cc:51:20: error: no match for 'operator==' (operand types are 'SECTION' and '__gnu_cxx::__alloc_traits<std::allocator<SECTION>, SECTION>::value_type' {aka 'SECTION'})
   51 |             if(now == sec[i].back()) {
      |                ~~~ ^~ ~~~~~~~~~~~~~
      |                |                 |
      |                SECTION           __gnu_cxx::__alloc_traits<std::allocator<SECTION>, SECTION>::value_type {aka SECTION}
In file included from /usr/include/c++/14/regex:68,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:181,
                 from a.cc:1:
/usr/include/c++/14/bits/regex.h:1103:5: note: candidate: 'template<class _BiIter> bool std::__cxx11::operator==(const sub_match<_BiIter>&, const sub_match<_BiIter>&)'
 1103 |     operator==(const sub_match<_BiIter>& __lhs, const sub_match<_BiIter>& __rhs)
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1103:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   'SECTION' is not derived from 'const std::__cxx11::sub_match<_BiIter>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
/usr/include/c++/14/bits/regex.h:1199:5: note: candidate: 'template<class _Bi_iter, class _Ch_traits, class _Ch_alloc> bool std::__cxx11::operator==(__sub_match_string<_Bi_iter, _Ch_traits, _Ch_alloc>&, const sub_match<_BiIter>&)'
 1199 |     operator==(const __sub_match_string<_Bi_iter, _Ch_traits, _Ch_alloc>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1199:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   'SECTION' is not derived from 'std::__cxx11::__sub_match_string<_Bi_iter, _Ch_traits, _Ch_alloc>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
/usr/include/c++/14/bits/regex.h:1274:5: note: candidate: 'template<class _Bi_iter, class _Ch_traits, class _Ch_alloc> bool std::__cxx11::operator==(const sub_match<_BiIter>&, __sub_match_string<_Bi_iter, _Ch_traits, _Ch_alloc>&)'
 1274 |     operator==(const sub_match<_Bi_iter>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1274:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   'SECTION' is not derived from 'const std::__cxx11::sub_match<_BiIter>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
/usr/include/c++/14/bits/regex.h:1366:5: note: candidate: 'template<class _Bi_iter> bool std::__cxx11::operator==(const typename std::iterator_traits<_Iter>::value_type*, const sub_match<_BiIter>&)'
 1366 |     operator==(typename iterator_traits<_Bi_iter>::value_type const* __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1366:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   '__gnu_cxx::__alloc_traits<std::allocator<SECTION>, SECTION>::value_type' {aka 'SECTION'} is not derived from 'const std::__cxx11::sub_match<_BiIter>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
/usr/include/c++/14/bits/regex.h:1441:5: note: candidate: 'template<class _Bi_iter> bool std::__cxx11::operator==(const sub_match<_BiIter>&, const typename std::iterator_traits<_Iter>::value_type*)'
 1441 |     operator==(const sub_match<_Bi_iter>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1441:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   'SECTION' is not derived from 'const std::__cxx11::sub_match<_BiIter>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
/usr/include/c++/14/bits/regex.h:1534:5: note: candidate: 'template<class _Bi_iter> bool std::__cxx11::operator==(const typename std::iterator_traits<_Iter>::value_type&, const sub_match<_BiIter>&)'
 1534 |     operator==(typename iterator_traits<_Bi_iter>::value_type const& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1534:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   '__gnu_cxx::__alloc_traits<std::allocator<SECTION>, SECTION>::value_type' {aka 'SECTION'} is not derived from 'const std::__cxx11::sub_match<_BiIter>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
/usr/include/c++/14/bits/regex.h:1613:5: note: candidate: 'template<class _Bi_iter> bool std::__cxx11::operator==(const sub_match<_BiIter>&, const typename std::iterator_traits<_Iter>::value_type&)'
 1613 |     operator==(const sub_match<_Bi_iter>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1613:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   'SECTION' is not derived from 'const std::__cxx11::sub_match<_BiIter>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
/usr/include/c++/14/bits/regex.h:2186:5: note: candidate: 'template<class _Bi_iter, class _Alloc> bool std::__cxx11::operator==(const match_results<_BiIter, _Alloc>&, const match_results<_BiIter, _Alloc>&)'
 2186 |     operator==(const match_results<_Bi_iter, _Alloc>& __m1,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:2186:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   'SECTION' is not derived from 'const std::__cxx11::match_results<_BiIter, _Alloc>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
In file included from /usr/include/c++/14/bits/stl_algobase.h:64,
                 from /usr/include/c++/14/algorithm:60,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:51:
/usr/include/c++/14/bits/stl_pair.h:1033:5: note: candidate: 'template<class _T1, class _T2> constexpr bool std::operator==(const pair<_T1, _T2>&, const pair<_T1, _T2>&)'
 1033 |     operator==(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_pair.h:1033:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   'SECTION' is not derived from 'const std::pair<_T1, _T2>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
In file included from /usr/include/c++/14/bits/stl_algobase.h:67:
/usr/include/c++/14/bits/stl_iterator.h:441:5: note: candidate: 'template<class _Iterator> constexpr bool std::operator==(const reverse_iterator<_Iterator>&, const reverse_iterator<_Iterator>&)'
  441 |     operator==(const reverse_iterator<_Iterator>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:441:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   'SECTION' is not derived from 'const std::reverse_iterator<_Iterator>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
/usr/include/c++/14/bits/stl_iterator.h:486:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr bool std::operator==(const reverse_iterator<_Iterator>&, const reverse_iterator<_IteratorR>&)'
  486 |     operator==(const reverse_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:486:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   'SECTION' is not derived from 'const std::reverse_iterator<_Iterator>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
/usr/include/c++/14/bits/stl_iterator.h:1667:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr bool std::operator==(const move_iterator<_IteratorL>&, const move_iterator<_IteratorR>&)'
 1667 |     operator==(const move_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1667:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   'SECTION' is not derived from 'const std::move_iterator<_IteratorL>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
/usr/include/c++/14/bits/stl_iterator.h:1737:5: note: candidate: 'template<class _Iterator> constexpr bool std::operator==(const move_iterator<_IteratorL>&, const move_iterator<_IteratorL>&)'
 1737 |     operator==(const move_iterator<_Iterator>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1737:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   'SECTION' is not derived from 'const std::move_iterator<_IteratorL>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
In file included from /usr/include/c++/14/bits/char_traits.h:42,
                 from /usr/include/c++/14/string:42,
                 from /usr/include/c++/14/bitset:52,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:52:
/usr/include/c++/14/bits/postypes.h:192:5: note: candidate: 'template<class _StateT> bool std::operator==(const fpos<_StateT>&, const fpos<_StateT>&)'
  192 |     operator==(const fpos<_StateT>& __lhs, const fpos<_StateT>& __rhs)
      |     ^~~~~~~~
/usr/include/c++/14/bits/postypes.h:192:5: note:   template argument deduction/substitution failed:
a.cc:51:35: note:   'SECTION' is not derived from 'const std::fpos<_StateT>'
   51 |             if(now == sec[i].back()) {
      |                                   ^
In file included from /usr/include/c++/14/string:43:
/usr/include/c++/14/bits/allocator.h:235:5: note: candidate: 'template<class _T1, class _T2> bool std::operator==(const allocator<_CharT>&, const allocator<_T2>&)'
  235 |     operator==(const allocator<_T1>&, const allocator<_T2>&)
      |     ^~~~~~~~
/usr/include/c++/14/bits/allocator.h:235:5: note:   te