Language: C++

/*
 /+==================================================+\
//+--------------------------------------------------+\\
|.|\\...>>>>>>> Hollwo_Pelw(ass) 's code <<<<<<<...//|.|
\\+--------------------------------------------------+//
 \+==================================================+/
*/
#include <bits/stdc++.h>
using namespace std;
// type
typedef long long ll;
typedef long double ld;
// loop
//#define For(i, l, r)        for (int i = l; i < r; i++)
//#define ForE(i, l, r)       for (int i = l; i <= r; i++)
//#define Ford(i, r, l)       for (int i = r; i > l; i--)
//#define FordE(i, r, l)      for (int i = r; i >= l; i--)
//#define Fora(i, a)          for (auto i : a)
// I/O
#define open(file, in, out) if (fopen(file in, "r")) {        \
                                freopen(file in, "r", stdin);  \
                                freopen(file out, "w", stdout); \
                            }
#define FAST_IO             std::ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define setpre(n)           fixed << setprecision(n)
// pair
#define F                   first
#define S                   second
#define pii                 pair<int, int>
#define pll                 pair<ll, ll>
#define pdd                 pair<ld, ld>
// vector & !!?(string)
#define eb                  emplace_back
#define pb                  push_back
#define all(a)              a.begin(), a.end()
#define rall(a)             a.rbegin(), a.rend()
#define sz(a)               a.size()
#define len(a)              a.length()
// geometry calculate
#define pi                  acos(-1.0)
#define g_sin(a)            sin(a*pi/180)
#define g_cos(a)            cos(a*pi/180)
#define g_tan(a)            tan(a*pi/180)
// set val
#define ms0(a)              memset(a,        0, sizeof(a));
#define ms1(a)              memset(a,        1, sizeof(a));
#define msn1(a)             memset(a,       -1, sizeof(a));
#define msinf(a)            memset(a, 0x3f3f3f, sizeof(a));
// constant
const int mod1 = 998244353, mod = 1e9+7;
const int MAXN = 100005, MAXM = 200010;
// code
#define int long long

int N, X, D;
map<int, vector<pii>> mp;
void Solve() {
    cin >> N >> X >> D;

    if (D == 0 && X == 0){
        cout << 1;
        return;
    }else if (D == 0){
        cout << N+1;
        return;
    }
    if (D < 0){
        D *= -1;
        X *= -1;
    }
    for (int k = 0; k <= n; k++){
        int s = k * (k - 1) / 2;
        int t = (n - k) * k + S;
        mp[(k*X)%D].eb(s, t);
    }
    int ans = 0;
    for (auto P:mp){
        pii A = P.S;
        sort(all(A));
        int mx = 0;
        for (auto pr:A){
            pr.F = max(pr.F, mx);
            if (pr.F <= pr.S){
                ans += pr.S - pr.F + 1;
            }
            mx = max(mx, pr.S);
        }
    }
    cout << ans;
}

signed main(){
    open("", ".inp", ".out");
    FAST_IO;
    int TC = 1;
    //cin >> TC;
    while(TC--) Solve();
    return 0;
}
/*

./-=====>>><<<-------- DEBUG -------->>><<<=====-\.
/.................................................\

+====================== INP ======================+


+====================== OUT ======================+


\................................................./
.\-=====>>><<<--------= END =-------->>><<<=====-/.
*/


Compiler output:
a.cc: In function 'void Solve()':
a.cc:71:26: error: 'n' was not declared in this scope
   71 |     for (int k = 0; k <= n; k++){
      |                          ^
a.cc:28:29: error: 'second' was not declared in this scope
   28 | #define S                   second
      |                             ^~~~~~
a.cc:73:31: note: in expansion of macro 'S'
   73 |         int t = (n - k) * k + S;
      |                               ^
a.cc:28:29: error: conversion from 'std::vector<std::pair<long long int, long long int> >' to non-scalar type 'std::pair<long long int, long long int>' requested
   28 | #define S                   second
      |                             ^
a.cc:78:19: note: in expansion of macro 'S'
   78 |         pii A = P.S;
      |                   ^
a.cc:35:31: error: 'struct std::pair<long long int, long long int>' has no member named 'begin'
   35 | #define all(a)              a.begin(), a.end()
      |                               ^~~~~
a.cc:79:14: note: in expansion of macro 'all'
   79 |         sort(all(A));
      |              ^~~
a.cc:35:42: error: 'struct std::pair<long long int, long long int>' has no member named 'end'
   35 | #define all(a)              a.begin(), a.end()
      |                                          ^~~
a.cc:79:14: note: in expansion of macro 'all'
   79 |         sort(all(A));
      |              ^~~
a.cc:81:22: error: no matching function for call to 'begin(std::pair<long long int, long long int>&)'
   81 |         for (auto pr:A){
      |                      ^
In file included from /usr/include/c++/14/bits/algorithmfwd.h:39,
                 from /usr/include/c++/14/bits/stl_algo.h:59,
                 from /usr/include/c++/14/algorithm:61,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:51,
                 from a.cc:8:
/usr/include/c++/14/initializer_list:88:5: note: candidate: 'template<class _Tp> constexpr const _Tp* std::begin(initializer_list<_Tp>)'
   88 |     begin(initializer_list<_Tp> __ils) noexcept
      |     ^~~~~
/usr/include/c++/14/initializer_list:88:5: note:   template argument deduction/substitution failed:
a.cc:81:22: note:   'std::pair<long long int, long long int>' is not derived from 'std::initializer_list<_Tp>'
   81 |         for (auto pr:A){
      |                      ^
In file included from /usr/include/c++/14/string:53,
                 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/range_access.h:52:5: note: candidate: 'template<class _Container> constexpr decltype (__cont.begin()) std::begin(_Container&)'
   52 |     begin(_Container& __cont) -> decltype(__cont.begin())
      |     ^~~~~
/usr/include/c++/14/bits/range_access.h:52:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/range_access.h: In substitution of 'template<class _Container> constexpr decltype (__cont.begin()) std::begin(_Container&) [with _Container = std::pair<long long int, long long int>]':
a.cc:81:22:   required from here
   81 |         for (auto pr:A){
      |                      ^
/usr/include/c++/14/bits/range_access.h:52:50: error: 'struct std::pair<long long int, long long int>' has no member named 'begin'
   52 |     begin(_Container& __cont) -> decltype(__cont.begin())
      |                                           ~~~~~~~^~~~~
/usr/include/c++/14/bits/range_access.h:63:5: note: candidate: 'template<class _Container> constexpr decltype (__cont.begin()) std::begin(const _Container&)'
   63 |     begin(const _Container& __cont) -> decltype(__cont.begin())
      |     ^~~~~
/usr/include/c++/14/bits/range_access.h:63:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/range_access.h: In substitution of 'template<class _Container> constexpr decltype (__cont.begin()) std::begin(const _Container&) [with _Container = std::pair<long long int, long long int>]':
a.cc:81:22:   required from here
   81 |         for (auto pr:A){
      |                      ^
/usr/include/c++/14/bits/range_access.h:63:56: error: 'const struct std::pair<long long int, long long int>' has no member named 'begin'
   63 |     begin(const _Container& __cont) -> decltype(__cont.begin())
      |                                                 ~~~~~~~^~~~~
/usr/include/c++/14/bits/range_access.h:95:5: note: candidate: 'template<class _Tp, long unsigned int _Nm> constexpr _Tp* std::begin(_Tp (&)[_Nm])'
   95 |     begin(_Tp (&__arr)[_Nm]) noexcept
      |     ^~~~~
/usr/include/c++/14/bits/range_access.h:95:5: note:   template argument deduction/substitution failed:
a.cc:81:22: note:   mismatched types '_Tp [_Nm]' and 'std::pair<long long int, long long int>'
   81 |         for (auto pr:A){
      |                      ^
In file included from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:166:
/usr/include/c++/14/valarray:1227:5: note: candidate: 'template<class _Tp> _Tp* std::begin(valarray<_Tp>&)'
 1227 |     begin(valarray<_Tp>& __va) noexcept
      |     ^~~~~
/usr/include/c++/14/valarray:1227:5: note:   template argument deduction/substitution failed:
a.cc:81:22: note:   'std::pair<long long int, long long int>' is not derived from 'std::valarray<_Tp>'
   81 |         for (auto pr:A){
      |                      ^
/usr/include/c++/14/valarray:1238:5: note: candidate: 'template<class _Tp> const _Tp* std::begin(const valarray<_Tp>&)'
 1238 |     begin(const valarray<_Tp>& __va) noexcept
      |     ^~~~~
/usr/include/c++/14/valarray:1238:5: note:   template argument deduction/substitution failed:
a.cc:81:22: note:   'std::pair<long long int, long long int>' is not derived from 'const std::valarray<_Tp>'
   81 |         for (auto pr:A){
      |                      ^
a.cc:81:22: error: no matching function for call to 'end(std::pair<long long int, long long int>&)'
/usr/include/c++/14/initializer_list:99:5: note: candidate: 'template<class _Tp> constexpr const _Tp* std::end(initializer_list<_Tp>)'
   99 |     end(initializer_list<_Tp> __ils) noexcept
      |     ^~~
/usr/include/c++/14/initializer_list:99:5: note:   template argument deduction/substitution failed:
a.cc:81:22: note:   'std::pair<long long int, long long int>' is not derived from 'std::initializer_list<_Tp>'
   81 |         for (auto pr:A){
      |                      ^
/usr/include/c++/14/bits/range_access.h:74:5: note: candidate: 'template<class _Container> constexpr decltype (__cont.end()) std::end(_Container&)'
   74 |     end(_Container& __cont) -> decltype(__cont.end())
      |     ^~~
/usr/include/c++/14/bits/range_access.h:74:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/range_access.h: In substitution of 'template<class _Container> constexpr decltype (__cont.end()) std::end(_Container&) [with _Container = std::pair<long long int, long long int>]':
a.cc:81:22:   required from here
   81 |         for (auto pr:A){
      |                      ^
/usr/include/c++/14/bits/range_access.h:74:48: error: 'struct std::pair<long long int, long long int>' has no member named 'end'
   74 |     end(_Container& __cont) -> decltype(__cont.end())
      |                                         ~~~~~~~^~~
/usr/include/c++/14/bits/range_access.h:85:5: note: candidate: 'template<class _Container> constexpr decltype (__cont.end()) std::end(const _Container&)'
   85 |     end(const _Container& __cont) -> decltype(__cont.end())
      |     ^~~
/usr/include/c++/14/bits/range_access.h:85:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/range_access.h: In substitution of 'template<class _Container> constexpr decltype (__cont.end()) std::end(const _Container&) [with _Container = std::pair<long long int, long long int>]':
a.cc:81:22:   required from here
   81 |         for (auto pr:A){
      |                      ^
/usr/include/c++/14/bits/range_access.h:85:54: error: 'const struct std::pair<long long int, long long int>' has no member named 'end'
   85 |     end(const _Container& __cont) -> decltype(__cont.end())
      |                                               ~~~~~~~^~~
/usr/include/c++/14/bits/range_access.h:106:5: note: candidate: 'template<class _Tp, long unsigned int _Nm> constexpr _Tp* std::end(_Tp (&)[_Nm])'
  106 |     end(_Tp (&__arr)[_Nm]) noexcept
      |     ^~~
/usr/include/c++/14/bits/range_access.h:106:5: note:   template argument deduction/substitution failed:
a.cc:81:22: note:   mismatched types '_Tp [_Nm]' and 'std::pair<long long int, long long int>'
   81 |         for (auto pr:A){
      |                      ^
/usr/include/c++/14/valarray:1249:5: note: candidate: 'template<class _Tp> _Tp* std::end(valarray<_Tp>&)'
 1249 |     end(valarray<_Tp>& __va) noexcept
      |     ^~~
/usr/include/c++/14/valarray:1249:5: note:   template argument deduction/substitution failed:
a.cc:81:22: note:   'std::pair<long long int, long long int>' is not derived from 'std::valarray<_Tp>'
   81 |         for (auto pr:A){
      |                      ^
/usr/include/c++/14/valarray:1265:5: note: candidate: 'template<class _Tp> const _Tp* std::end(const valarray<_Tp>&)'
 1265 |     end(const valarray<_Tp>& __va) noexcept
      |     ^~~
/usr/include/c++/14/valarray:1265:5: note:   template argument deduction/substitution failed:
a.cc:81:22: note:   'std::pair<long long int, long long int>' is not derived from 'const std::valarray<_Tp>'
   81 |         for (auto pr:A){
      |                      ^