#line 1 "verify/math/UNIT_fraction.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (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())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"
#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <class T, class S = T>
S SUM(const vector<T>& a) {
return accumulate(ALL(a), S(0));
}
template <class T>
inline bool chmin(T& a, T b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T>
inline bool chmax(T& a, T b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <class T>
int popcnt(T x) {
return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"
#line 2 "template/inout.hpp"
struct Fast {
Fast() {
cin.tie(nullptr);
ios_base::sync_with_stdio(false);
cout << fixed << setprecision(15);
}
} fast;
ostream& operator<<(ostream& os, __uint128_t x) {
char buf[40];
size_t k = 0;
while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10;
if (k == 0) buf[k++] = '0';
while (k) os << buf[--k];
return os;
}
ostream& operator<<(ostream& os, __int128_t x) {
return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x);
}
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
for (auto& v : a) is >> v;
return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
for (auto it = a.begin(); it != a.end();) {
os << *it;
if (++it != a.end()) os << " ";
}
return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
os << "{";
for (auto it = st.begin(); it != st.end();) {
os << *it;
if (++it != st.end()) os << ",";
}
os << "}";
return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
os << "{";
for (auto it = mp.begin(); it != mp.end();) {
os << it->first << ":" << it->second;
if (++it != mp.end()) os << ",";
}
os << "}";
return os;
}
void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T& t, const U&... u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
namespace IO {
namespace Graph {
vector<vector<int>> unweighted(int n, int m, bool directed = false, int offset = 1) {
vector<vector<int>> g(n);
for (int i = 0; i < m; i++) {
int u, v;
cin >> u >> v;
u -= offset, v -= offset;
g[u].push_back(v);
if (!directed) g[v].push_back(u);
}
return g;
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, int m, bool directed = false, int offset = 1) {
vector<vector<pair<int, T>>> g(n);
for (int i = 0; i < m; i++) {
int u, v;
T w;
cin >> u >> v >> w;
u -= offset, v -= offset;
g[u].push_back({v, w});
if (!directed) g[v].push_back({u, w});
}
return g;
}
} // namespace Graph
namespace Tree {
vector<vector<int>> unweighted(int n, bool directed = false, int offset = 1) {
return Graph::unweighted(n, n - 1, directed, offset);
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, bool directed = false, int offset = 1) {
return Graph::weighted<T>(n, n - 1, directed, offset);
}
vector<vector<int>> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) {
vector<vector<int>> g(n);
for (int i = 1; i < n; i++) {
int p;
cin >> p;
p -= offset;
if (to_root) g[i].push_back(p);
if (to_leaf) g[p].push_back(i);
}
return g;
}
} // namespace Tree
} // namespace IO
#line 10 "template/template.hpp"
#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int i, T name) {
cerr << '\n';
}
template <class T1, class T2, class... 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...);
}
#line 2 "math/fraction.hpp"
template <class T>
struct Fraction {
T a, b;
Fraction() : a(0), b(1) {}
Fraction(T _a) : a(_a), b(1) {}
Fraction(T _a, T _b) { init(_a, _b); }
T floor() const { return a >= 0 ? a / b : (a + 1) / b - 1; }
T ceil() const { return a > 0 ? (a - 1) / b + 1 : a / b; }
template <class V>
V get() const { return V(a) / b; }
using frac = Fraction;
static frac raw(T _a, T _b) {
frac x;
x.a = _a, x.b = _b;
return x;
}
frac& init(T _a, T _b) {
T g = gcd(_a, _b);
a = _a / g, b = _b / g;
if (b < 0) a = -a, b = -b;
return *this;
}
frac inv() const { return a >= 0 ? raw(b, a) : raw(-b, -a); }
frac operator-() const { return frac(-a, b); }
frac& operator+=(const frac& x) { return init(a * x.b + x.a * b, b * x.b); }
frac& operator-=(const frac& x) { return init(a * x.b - x.a * b, b * x.b); }
frac& operator*=(const frac& x) { return init(a * x.a, b * x.b); }
frac& operator/=(const frac& x) { return init(a * x.b, b * x.a); }
frac operator+(const frac& x) const { return frac(*this) += x; }
frac operator-(const frac& x) const { return frac(*this) -= x; }
frac operator*(const frac& x) const { return frac(*this) *= x; }
frac operator/(const frac& x) const { return frac(*this) /= x; }
bool operator<(const frac& x) const { return a * x.b < b * x.a; }
bool operator>(const frac& x) const { return a * x.b > b * x.a; }
bool operator<=(const frac& x) const { return a * x.b <= b * x.a; }
bool operator>=(const frac& x) const { return a * x.b >= b * x.a; }
bool operator==(const frac& x) const { return a * x.b == b * x.a; }
bool operator!=(const frac& x) const { return a * x.b != b * x.a; }
friend istream& operator>>(istream& is, frac& x) { return is >> x.a >> x.b; }
friend ostream& operator<<(ostream& os, const frac& x) { return os << x.a << '/' << x.b; }
};
/**
* @brief 有理数
*/
#line 2 "math/simple-fraction.hpp"
template <class T>
struct SimpleFraction {
T a, b;
SimpleFraction() : a(0), b(1) {}
SimpleFraction(T _a) : a(_a), b(1) {}
SimpleFraction(T _a, T _b) { init(_a, _b); }
template <class V>
V get() const { return V(a) / b; }
using frac = SimpleFraction;
frac &init(T _a, T _b) {
a = _a, b = _b;
if (b < 0) a = -a, b = -b;
if (a == 0) b = 1;
return *this;
}
frac operator-() const { return frac(-a, b); }
frac &operator+=(const frac &x) { return init(a * x.b + x.a * b, b * x.b); }
frac &operator-=(const frac &x) { return init(a * x.b - x.a * b, b * x.b); }
frac &operator*=(const frac &x) { return init(a * x.a, b * x.b); }
frac &operator/=(const frac &x) { return init(a * x.b, b * x.a); }
frac operator+(const frac &x) const { return frac(*this) += x; }
frac operator-(const frac &x) const { return frac(*this) -= x; }
frac operator*(const frac &x) const { return frac(*this) *= x; }
frac operator/(const frac &x) const { return frac(*this) /= x; }
bool operator<(const frac &x) const { return a * x.b < b * x.a; }
bool operator>(const frac &x) const { return a * x.b > b * x.a; }
bool operator<=(const frac &x) const { return a * x.b <= b * x.a; }
bool operator>=(const frac &x) const { return a * x.b >= b * x.a; }
bool operator==(const frac &x) const { return a * x.b == b * x.a; }
bool operator!=(const frac &x) const { return a * x.b != b * x.a; }
friend istream &operator>>(istream &is, frac &x) { return is >> x.a >> x.b; }
friend ostream &operator<<(ostream &os, const frac &x) { return os << x.a << '/' << x.b; }
};
/**
* @brief 有理数 (約分なし)
*/
#line 6 "verify/math/UNIT_fraction.test.cpp"
void check_fraction(Fraction<ll> x) {
assert(x.b > 0);
assert(gcd(abs(x.a), abs(x.b)) == 1);
}
void test_fraction() {
rep(a, -20, 21) rep(b, 1, 21) {
Fraction<ll> x(a, b);
check_fraction(x);
assert(x == Fraction<ll>(a * 3, b * 3));
if (a != 0) assert(x * x.inv() == Fraction<ll>(1));
Fraction<ll> y(b - 10, b + 1);
check_fraction(x + y);
check_fraction(x - y);
check_fraction(x * y);
if (y.a != 0) check_fraction(x / y);
long double v = x.get<long double>();
assert(x.floor() <= v && v < x.floor() + 1);
assert(x.ceil() - 1 < v && v <= x.ceil());
}
}
void test_simple_fraction() {
SimpleFraction<ll> x(1, 2), y(1, 3);
assert(x + y == SimpleFraction<ll>(5, 6));
assert(x - y == SimpleFraction<ll>(1, 6));
assert(x * y == SimpleFraction<ll>(1, 6));
assert(x / y == SimpleFraction<ll>(3, 2));
assert(SimpleFraction<ll>(-1, -2) == SimpleFraction<ll>(1, 2));
assert(SimpleFraction<ll>(0, 100).b == 1);
}
int main() {
test_fraction();
test_simple_fraction();
int a, b;
in(a, b);
out(a + b);
}
verify/math/UNIT_fraction.test.cpp