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test/1_mytest/count_lattice_point_in_convex_polygon.test.cpp
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- Last update: 2025-07-03 18:22:07+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
Depends on
- convex/lattice_point_count.hpp
- convex/line_min_function.hpp
- geo/base.hpp
- geo/convex_hull.hpp
- mod/floor_sum_of_linear.hpp
- my_template.hpp
- random/base.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "random/base.hpp"
#include "convex/lattice_point_count.hpp"
void test() {
ll N = RNG(0, 7);
vc<tuple<ll, ll, ll>> LINE;
FOR(N) {
while (1) {
ll a = RNG(-3, 4);
ll b = RNG(-3, 4);
if (a == 0 && b == 0) continue;
ll c = RNG(-30, 31);
LINE.eb(a, b, c);
break;
}
}
ll K = 200;
ll god = 0;
FOR(x, -2 * K, 2 * K + 1) {
ll mi = -infty<ll>, ma = infty<ll>;
for (auto& [a, b, c]: LINE) {
if (b == 0) {
if (a * x <= c) continue;
mi = infty<ll> + 1;
break;
}
if (b > 0) { chmin(ma, floor<ll>(c - a * x, b)); }
if (b < 0) { chmax(mi, ceil<ll>(a * x - c, -b)); }
}
if (mi > ma) continue;
if (abs(x) >= K || mi == -infty<ll> || ma == infty<ll>) {
god = 0;
break;
}
god += ma - mi + 1;
}
ll ANS = lattice_point_count(LINE);
assert(god == ANS);
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
FOR(100000) test();
solve();
return 0;
}#line 1 "test/1_mytest/count_lattice_point_in_convex_polygon.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
// https://codeforces.com/blog/entry/96344
// https://codeforces.com/blog/entry/126772?#comment-1154880
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq_max = priority_queue<T>;
template <class T>
using pq_min = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a) - 1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a) - 1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b) - 1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T kth_bit(int k) {
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
return x >> k & 1;
}
template <typename UINT>
struct all_bit {
struct iter {
UINT s;
iter(UINT s) : s(s) {}
int operator*() const { return lowbit(s); }
iter &operator++() {
s &= s - 1;
return *this;
}
bool operator!=(const iter) const { return s != 0; }
};
UINT s;
all_bit(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
template <typename UINT>
struct all_subset {
static_assert(is_unsigned<UINT>::value);
struct iter {
UINT s, t;
bool ed;
iter(UINT s) : s(s), t(s), ed(0) {}
int operator*() const { return s ^ t; }
iter &operator++() {
(t == 0 ? ed = 1 : t = (t - 1) & s);
return *this;
}
bool operator!=(const iter) const { return !ed; }
};
UINT s;
all_subset(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const U &A) {
return std::accumulate(A.begin(), A.end(), T{});
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq_min<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pq_max<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &...others) {
vc<T> &res = first;
(res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 4 "test/1_mytest/count_lattice_point_in_convex_polygon.test.cpp"
#line 2 "random/base.hpp"
u64 RNG_64() {
static u64 x_ = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL;
x_ ^= x_ << 7;
return x_ ^= x_ >> 9;
}
u64 RNG(u64 lim) { return RNG_64() % lim; }
ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 2 "convex/line_min_function.hpp"
#line 2 "geo/convex_hull.hpp"
#line 2 "geo/base.hpp"
template <typename T>
struct Point {
T x, y;
Point() : x(0), y(0) {}
template <typename A, typename B>
Point(A x, B y) : x(x), y(y) {}
template <typename A, typename B>
Point(pair<A, B> p) : x(p.fi), y(p.se) {}
Point operator+=(const Point p) {
x += p.x, y += p.y;
return *this;
}
Point operator-=(const Point p) {
x -= p.x, y -= p.y;
return *this;
}
Point operator+(Point p) const { return {x + p.x, y + p.y}; }
Point operator-(Point p) const { return {x - p.x, y - p.y}; }
bool operator==(Point p) const { return x == p.x && y == p.y; }
bool operator!=(Point p) const { return x != p.x || y != p.y; }
Point operator-() const { return {-x, -y}; }
Point operator*(T t) const { return {x * t, y * t}; }
Point operator/(T t) const { return {x / t, y / t}; }
bool operator<(Point p) const {
if (x != p.x) return x < p.x;
return y < p.y;
}
T dot(const Point& other) const { return x * other.x + y * other.y; }
T det(const Point& other) const { return x * other.y - y * other.x; }
double norm() { return sqrtl(x * x + y * y); }
double angle() { return atan2(y, x); }
Point rotate(double theta) {
static_assert(!is_integral<T>::value);
double c = cos(theta), s = sin(theta);
return Point{c * x - s * y, s * x + c * y};
}
Point rot90(bool ccw) { return (ccw ? Point{-y, x} : Point{y, -x}); }
};
#ifdef FASTIO
template <typename T>
void rd(Point<T>& p) {
fastio::rd(p.x), fastio::rd(p.y);
}
template <typename T>
void wt(Point<T>& p) {
fastio::wt(p.x);
fastio::wt(' ');
fastio::wt(p.y);
}
#endif
// A -> B -> C と進むときに、左に曲がるならば +1、右に曲がるならば -1
template <typename T>
int ccw(Point<T> A, Point<T> B, Point<T> C) {
T x = (B - A).det(C - A);
if (x > 0) return 1;
if (x < 0) return -1;
return 0;
}
template <typename REAL, typename T, typename U>
REAL dist(Point<T> A, Point<U> B) {
REAL dx = REAL(A.x) - REAL(B.x);
REAL dy = REAL(A.y) - REAL(B.y);
return sqrt(dx * dx + dy * dy);
}
// ax+by+c
template <typename T>
struct Line {
T a, b, c;
Line(T a, T b, T c) : a(a), b(b), c(c) {}
Line(Point<T> A, Point<T> B) { a = A.y - B.y, b = B.x - A.x, c = A.x * B.y - A.y * B.x; }
Line(T x1, T y1, T x2, T y2) : Line(Point<T>(x1, y1), Point<T>(x2, y2)) {}
template <typename U>
U eval(Point<U> P) {
return U(a) * P.x + U(b) * P.y + U(c);
}
template <typename U>
T eval(U x, U y) {
return a * x + b * y + c;
}
// 同じ直線が同じ a,b,c で表現されるようにする
void normalize() {
static_assert(is_same_v<T, int> || is_same_v<T, long long>);
T g = gcd(gcd(abs(a), abs(b)), abs(c));
a /= g, b /= g, c /= g;
if (b < 0) { a = -a, b = -b, c = -c; }
if (b == 0 && a < 0) { a = -a, b = -b, c = -c; }
}
bool is_parallel(Line other) { return a * other.b - b * other.a == 0; }
bool is_orthogonal(Line other) { return a * other.a + b * other.b == 0; }
};
template <typename T>
struct Segment {
Point<T> A, B;
Segment(Point<T> A, Point<T> B) : A(A), B(B) {}
Segment(T x1, T y1, T x2, T y2) : Segment(Point<T>(x1, y1), Point<T>(x2, y2)) {}
bool contain(Point<T> C) {
T det = (C - A).det(B - A);
if (det != 0) return 0;
return (C - A).dot(B - A) >= 0 && (C - B).dot(A - B) >= 0;
}
Line<T> to_Line() { return Line(A, B); }
};
template <typename REAL>
struct Circle {
Point<REAL> O;
REAL r;
Circle() {}
Circle(Point<REAL> O, REAL r) : O(O), r(r) {}
Circle(REAL x, REAL y, REAL r) : O(x, y), r(r) {}
template <typename T>
bool contain(Point<T> p) {
REAL dx = p.x - O.x, dy = p.y - O.y;
return dx * dx + dy * dy <= r * r;
}
};
#line 4 "geo/convex_hull.hpp"
// allow_180=true で同一座標点があるとこわれる
// full なら I[0] が sorted で min になる
template <typename T, bool allow_180 = false>
vector<int> ConvexHull(vector<Point<T>>& XY, string mode = "full", bool sorted = false) {
assert(mode == "full" || mode == "lower" || mode == "upper");
ll N = XY.size();
if (N == 1) return {0};
if (N == 2) {
if (XY[0] < XY[1]) return {0, 1};
if (XY[1] < XY[0]) return {1, 0};
return {0};
}
vc<int> I(N);
if (sorted) {
FOR(i, N) I[i] = i;
} else {
I = argsort(XY);
}
if constexpr (allow_180) { FOR(i, N - 1) assert(XY[i] != XY[i + 1]); }
auto check = [&](ll i, ll j, ll k) -> bool {
T det = (XY[j] - XY[i]).det(XY[k] - XY[i]);
if constexpr (allow_180) return det >= 0;
return det > T(0);
};
auto calc = [&]() {
vector<int> P;
for (auto&& k: I) {
while (P.size() > 1) {
auto i = P[P.size() - 2];
auto j = P[P.size() - 1];
if (check(i, j, k)) break;
P.pop_back();
}
P.eb(k);
}
return P;
};
vc<int> P;
if (mode == "full" || mode == "lower") {
vc<int> Q = calc();
P.insert(P.end(), all(Q));
}
if (mode == "full" || mode == "upper") {
if (!P.empty()) P.pop_back();
reverse(all(I));
vc<int> Q = calc();
P.insert(P.end(), all(Q));
}
if (mode == "upper") reverse(all(P));
while (len(P) >= 2 && XY[P[0]] == XY[P.back()]) P.pop_back();
return P;
}
#line 4 "convex/line_min_function.hpp"
// 1 次関数の max を [L,R,a,b] の列として出力
// https://qoj.ac/contest/1576/problem/8505
template <typename Re, typename T>
vc<tuple<Re, Re, Re, Re>> line_min_function_real(vc<pair<T, T>> LINE) {
assert(!LINE.empty());
using P = Point<T>;
vc<P> point;
for (auto& [x, y]: LINE) point.eb(P(x, y));
auto I = ConvexHull(point, "lower");
point = rearrange(point, I);
int N = len(point);
if (N >= 2 && point[N - 1].x == point[N - 2].x) { POP(point), --N; }
reverse(all(point)); // 傾きは大きい方から
Re l = -infty<Re>;
vc<tuple<Re, Re, Re, Re>> ANS;
FOR(i, N) {
Re r = infty<Re>;
auto [a, b] = point[i];
if (i + 1 < N) {
auto [c, d] = point[i + 1];
if (a == c) continue;
assert(a > c);
r = Re(d - b) / (a - c);
chmax(r, l), chmin(r, infty<Re>);
}
if (l < r) ANS.eb(l, r, a, b), l = r;
}
return ANS;
}
// 1 次関数の max を [L,R,a,b] の列として出力
template <typename Re, typename T>
vc<tuple<Re, Re, Re, Re>> line_max_function_real(vc<pair<T, T>> LINE) {
assert(!LINE.empty());
for (auto& [a, b]: LINE) a = -a, b = -b;
auto ANS = line_min_function_real<Re, T>(LINE);
for (auto& [l, r, a, b]: ANS) a = -a, b = -b;
return ANS;
}
// LINE(a,b,c): y=(ax+b)/c, 評価点は整数
// 1 次関数の min を [L,R,a,b,c] の列として出力
// オーバーフロー安全
vc<tuple<ll, ll, ll, ll, ll>> line_min_function_rational(vc<tuple<ll, ll, ll>> LINE, ll L, ll R) {
// 傾き降順
sort(all(LINE), [&](auto& L, auto& R) -> bool {
auto& [a1, b1, c1] = L;
auto& [a2, b2, c2] = R;
return i128(a1) * c2 > i128(a2) * c1;
});
vc<tuple<ll, ll, ll, ll, ll>> ANS;
for (auto& [a2, b2, c2]: LINE) {
while (1) {
if (ANS.empty()) {
ANS.eb(L, R, a2, b2, c2);
break;
}
auto& [L1, R1, a1, b1, c1] = ANS.back();
i128 s = i128(c2) * a1 - i128(a2) * c1; // >= 0
i128 t = i128(b2) * c1 - i128(b1) * c2;
if (s == 0) {
// 平行なので小さい方だけを残す
if (t >= 0) break;
ANS.pop_back();
if (len(ANS)) get<1>(ANS.back()) = R;
continue;
}
i128 x = ceil<i128>(t, s);
// x 以上で 2 の方が下に来る
if (x <= L1) {
ANS.pop_back();
continue;
}
if (x < R) {
R1 = x;
ANS.eb(x, R, a2, b2, c2);
break;
} else {
break;
}
}
}
return ANS;
}
// LINE(a,b,c): y=(ax+b)/c, 評価点は整数
// 1 次関数の max を [L,R,a,b,c] の列として出力
// オーバーフロー安全
vc<tuple<ll, ll, ll, ll, ll>> line_max_function_rational(vc<tuple<ll, ll, ll>> LINE, ll L, ll R) {
for (auto& [a, b, c]: LINE) a = -a, b = -b;
auto ANS = line_min_function_rational(LINE, L, R);
for (auto& [L, R, a, b, c]: ANS) a = -a, b = -b;
return ANS;
}
// LINE(a,b): y=ax+b, 評価点は整数
// 1 次関数の min を [L,R,a,b] の列として出力
// オーバーフロー安全
vc<tuple<ll, ll, ll, ll>> line_min_function_integer(vc<pair<ll, ll>> LINE, ll L, ll R) {
// 傾き降順
sort(all(LINE), [&](auto& L, auto& R) -> bool {
auto& [a1, b1] = L;
auto& [a2, b2] = R;
return a1 > a2;
});
vc<tuple<ll, ll, ll, ll>> ANS;
for (auto& [a2, b2]: LINE) {
while (1) {
if (ANS.empty()) {
ANS.eb(L, R, a2, b2);
break;
}
auto& [L1, R1, a1, b1] = ANS.back();
if (a1 == a2) {
if (b1 <= b2) break;
ANS.pop_back();
if (len(ANS)) get<1>(ANS.back()) = R;
continue;
}
ll x = ceil<ll>(b2 - b1, a1 - a2);
// x 以上で 2 の方が下に来る
if (x <= L1) {
ANS.pop_back();
continue;
}
if (x < R) {
R1 = x;
ANS.eb(x, R, a2, b2);
break;
} else {
break;
}
}
}
return ANS;
}
// LINE(a,b,c): y=(ax+b)/c, 評価点は整数
// 1 次関数の min を [L,R,a,b,c] の列として出力
// c>0, (ax+b)c がオーバーフローしない,
vc<tuple<ll, ll, ll, ll>> line_max_function_integer(vc<pair<ll, ll>> LINE, ll L, ll R) {
for (auto& [a, b]: LINE) a = -a, b = -b;
auto ANS = line_min_function_integer(LINE, L, R);
for (auto& [L, R, a, b]: ANS) a = -a, b = -b;
return ANS;
}
// (L,R,func) の下側と上側をマージするときなどに使う用
template <typename T>
vc<tuple<T, T, T, T, T, T>> merge_46(vc<tuple<T, T, T, T>> A, vc<tuple<T, T, T, T>> B) {
vc<tuple<T, T, T, T, T, T>> ANS;
reverse(all(A));
reverse(all(B));
while (len(A) && len(B)) {
auto& [l1, r1, a1, b1] = A.back();
auto& [l2, r2, a2, b2] = B.back();
assert(l1 == l2);
T r = min(r1, r2);
ANS.eb(l1, r, a1, b1, a2, b2);
l1 = r, l2 = r;
if (r1 == r) POP(A);
if (r2 == r) POP(B);
};
return ANS;
}
// (L,R,func) の下側と上側をマージするときなどに使う用
// f(L,R,a1,b1,a2,b2)
template <typename T, typename F>
void merge_46(const vc<tuple<T, T, T, T>>& A, const vc<tuple<T, T, T, T>>& B, F f) {
int i = 0, j = 0;
while (i < len(A) && j < len(B)) {
auto& [l1, r1, a1, b1] = A[i];
auto& [l2, r2, a2, b2] = B[j];
T l = max(l1, l2), r = min(r1, r2);
if (l < r) f(l, r, a1, b1, a2, b2);
(r1 < r2 ? i : j)++;
}
}
// (L,R,func) の下側と上側をマージするときなどに使う用
// f(L,R,a1,b1,a2,b2)
template <typename T, typename F>
void merge_58(const vc<tuple<T, T, T, T, T>>& A, const vc<tuple<T, T, T, T, T>>& B, F f) {
int i = 0, j = 0;
while (i < len(A) && j < len(B)) {
auto& [l1, r1, a1, b1, c1] = A[i];
auto& [l2, r2, a2, b2, c2] = B[j];
T l = max(l1, l2), r = min(r1, r2);
if (l < r) f(l, r, a1, b1, c1, a2, b2, c2);
(r1 < r2 ? i : j)++;
}
}
#line 2 "mod/floor_sum_of_linear.hpp"
// sum_{x in [L,R)} floor(ax + b, mod)
// I は範囲内で ax+b がオーバーフローしない程度
template <typename O = i128, typename I = long long>
O floor_sum_of_linear(I L, I R, I a, I b, I mod) {
assert(L <= R);
O res = 0;
b += L * a;
I N = R - L;
if (b < 0) {
I k = ceil(-b, mod);
b += k * mod;
res -= O(N) * O(k);
}
while (N) {
I q;
tie(q, a) = divmod(a, mod);
res += (N & 1 ? O(N) * O((N - 1) / 2) * O(q) : O(N / 2) * O(N - 1) * O(q));
if (b >= mod) {
tie(q, b) = divmod(b, mod);
res += O(N) * q;
}
tie(N, b) = divmod(a * N + b, mod);
tie(a, mod) = mp(mod, a);
}
return res;
}
#line 3 "convex/lattice_point_count.hpp"
// ax+by<=c という半平面たち
// 有界でないときは 0 を返す
// （格子点が 0 個ということはあるので答えが inf とは限らない）
// 入力が pow(10,18) 以下とかであればオーバーフローしないつもり
i128 lattice_point_count(vc<tuple<ll, ll, ll>> LINE) {
ll L = -infty<ll>, R = infty<ll>;
vc<tuple<ll, ll, ll>> LINE1, LINE2;
for (auto& [a, b, c]: LINE) {
if (b == 0) {
assert(a != 0);
if (a > 0) { chmin(R, floor<ll>(c, a) + 1); }
elif (a < 0) { chmax(L, ceil<ll>(-c, -a)); }
} else {
if (b > 0) { LINE2.eb(-a, c, b); }
if (b < 0) { LINE1.eb(a, -c, -b); }
}
}
if (L >= R) return 0;
if (LINE1.empty() || LINE2.empty()) return 0;
auto LOWER = line_max_function_rational(LINE1, L, R);
auto UPPER = line_min_function_rational(LINE2, L, R);
i128 ANS = 0;
bool bad = 0;
auto wk = [&](ll L, ll R, ll a1, ll b1, ll c1, ll a2, ll b2, ll c2) -> void {
// 交点 t/s
i128 s = i128(a2) * c1 - i128(a1) * c2;
i128 t = i128(b1) * c2 - i128(b2) * c1;
if (s == 0) {
if (t > 0) return;
}
if (s > 0) { chmax(L, ceil<i128>(t, s)); }
if (s < 0) { chmin(R, floor<i128>(-t, -s) + 1); }
if (L >= R) return;
if (L == -infty<ll> || R == infty<ll>) {
bad = 1;
return;
}
ANS += floor_sum_of_linear<i128, i128>(L, R, a2, b2, c2);
ANS -= floor_sum_of_linear<i128, i128>(L, R, a1, b1 - 1, c1);
};
merge_58(LOWER, UPPER, wk);
if (bad) return 0;
return ANS;
}
#line 7 "test/1_mytest/count_lattice_point_in_convex_polygon.test.cpp"
void test() {
ll N = RNG(0, 7);
vc<tuple<ll, ll, ll>> LINE;
FOR(N) {
while (1) {
ll a = RNG(-3, 4);
ll b = RNG(-3, 4);
if (a == 0 && b == 0) continue;
ll c = RNG(-30, 31);
LINE.eb(a, b, c);
break;
}
}
ll K = 200;
ll god = 0;
FOR(x, -2 * K, 2 * K + 1) {
ll mi = -infty<ll>, ma = infty<ll>;
for (auto& [a, b, c]: LINE) {
if (b == 0) {
if (a * x <= c) continue;
mi = infty<ll> + 1;
break;
}
if (b > 0) { chmin(ma, floor<ll>(c - a * x, b)); }
if (b < 0) { chmax(mi, ceil<ll>(a * x - c, -b)); }
}
if (mi > ma) continue;
if (abs(x) >= K || mi == -infty<ll> || ma == infty<ll>) {
god = 0;
break;
}
god += ma - mi + 1;
}
ll ANS = lattice_point_count(LINE);
assert(god == ANS);
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
FOR(100000) test();
solve();
return 0;
}