#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) (x) #define dbgif(cond, x) 0 #endif // Rational number + {infinity(1 / 0), -infiity(-1 / 0)} (有理数) struct Rational { using Int = long long int; // __int128 Int num, den; static Int my_gcd(Int a, Int b) { // return __gcd(a, b); if (a < 0) a = -a; if (b < 0) b = -b; while (a and b) { if (a > b) a %= b; else b %= a; } return a + b; } Rational(Int num = 0, Int den = 1) : num(num), den(den) { normalize(); } void normalize() { // reduction and making denominator nonnegative Int g = my_gcd(num, den); num /= g, den /= g; if (den < 0) num = -num, den = -den; } Rational operator+(const Rational &r) const { return Rational(num * r.den + den * r.num, den * r.den); } Rational operator-(const Rational &r) const { return Rational(num * r.den - den * r.num, den * r.den); } Rational operator*(const Rational &r) const { return Rational(num * r.num, den * r.den); } Rational operator/(const Rational &r) const { return Rational(num * r.den, den * r.num); } Rational &operator+=(const Rational &r) { return *this = *this + r; } Rational &operator-=(const Rational &r) { return *this = *this - r; } Rational &operator*=(const Rational &r) { return *this = *this * r; } Rational &operator/=(const Rational &r) { return *this = *this / r; } Rational operator-() const { return Rational(-num, den); } Rational abs() const { return Rational(num > 0 ? num : -num, den); } bool operator==(const Rational &r) const { return num == r.num and den == r.den; } bool operator!=(const Rational &r) const { return num != r.num or den != r.den; } bool operator<(const Rational &r) const { if (den == 0 and r.den == 0) return num < r.num; else if (den == 0) return num < 0; else if (r.den == 0) return r.num > 0; else return num * r.den < den * r.num; } bool operator<=(const Rational &r) const { return (*this == r) or (*this < r); } bool operator>(const Rational &r) const { return r < *this; } bool operator>=(const Rational &r) const { return (r == *this) or (r < *this); } explicit operator double() const { return (double)num / (double)den; } explicit operator long double() const { return (long double)num / (long double)den; } friend std::ostream &operator<<(std::ostream &os, const Rational &x) { return os << x.num << '/' << x.den; } }; int main() { lint N, M, K; cin >> N >> M >> K; Rational r1(M * (M - 1), N * (N - 1 - K)), r2((N - M) * M, N * (N - 1 - K)); auto r = r1 + r2; cout << r.num << ' ' << r.den << '\n'; }