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#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_floor_of_linear" #include "Template/template.hpp" #include "Math/floorsum.hpp" int main(){ int t; cin>>t; while(t--){ int n,m,a,b; cin>>n>>m>>a>>b; cout<<FloorSum(n,a,b,m)<<'\n'; } return 0; }
#line 1 "Verify/LC_sum_of_floor_of_linear.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/sum_of_floor_of_linear" #line 1 "Template/template.hpp" #include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++) #define rrep(i, a, b) for (int i = (int)(b-1); i >= (int)(a); i--) #define ALL(v) (v).begin(), (v).end() #define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()) #define SZ(v) (int)v.size() #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin()) #define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin()) using uint = unsigned int; using ll = long long int; using ull = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; template <typename T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return 1; } return 0; } template <typename T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return 1; } return 0; } template <typename T, typename U> T ceil(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? (x + y - 1) / y : x / y); } template <typename T, typename U> T floor(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? x / y : (x - y + 1) / y); } template <typename T> int popcnt(T x) { return __builtin_popcountll(x); } template <typename T> int topbit(T x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } template <typename T> int lowbit(T x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } #ifdef LOCAL #define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__) #else #define show(...) true #endif template <typename T> void _show(int i, T name) { cerr << '\n'; } template <typename T1, typename T2, typename... T3> void _show(int i, const T1 &a, const T2 &b, const T3 &...c) { for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i]; cerr << ":" << b << " "; _show(i + 1, a, c...); } template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << "P(" << p.first << ", " << p.second << ")"; return os; } template <typename T, template <class> class C> ostream &operator<<(ostream &os, const C<T> &v) { os << "["; for (auto d : v) os << d << ", "; os << "]"; return os; } #line 2 "Math/floorsum.hpp" template<typename T=ll>T FloorSum(ll n,ll a,ll b,ll m){ //sum_{k=0}^{n-1} [(a*k+b)/m] T res=0; if(a>=m)res+=T(a/m)*n*(n-1)/2,a-=a/m*m; else if(a<0)res-=T((-a+m-1)/m)*n*(n-1)/2,a+=((-a+m-1)/m)*m; if(b>=m)res+=(b/m)*n,b-=b/m*m; else if(b<0)res-=((-b+m-1)/m)*n,b+=((-b+m-1)/m)*m; while(1){ ll y_max=a*n+b; if(y_max<m)break; n=y_max/m; b=y_max%m; res+=(n*(n-1)/2)*(m/a)+n*(b/a); swap(m,a); a=a%m; b=b%m; } return res; } /** * @brief Floor Sum * @docs docs/floorsum.md */ #line 5 "Verify/LC_sum_of_floor_of_linear.test.cpp" int main(){ int t; cin>>t; while(t--){ int n,m,a,b; cin>>n>>m>>a>>b; cout<<FloorSum(n,a,b,m)<<'\n'; } return 0; }