2182.cpp

#include <bits/stdc++.h>

using namespace std;

#define print_op(...) ostream& operator<<(ostream& out, const __VA_ARGS__& u)
template<typename A, typename B> print_op(pair<A, B>) { return out << "(" << u.first << ", " << u.second << ")"; }
template<typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type> print_op(T_container) { out << "{"; string sep; for (const T &x : u) out << sep << x, sep = ", "; return out << "}"; }
template<typename T> void dbg_out(string s, T x) {cerr << "\033[1;35m" << s << "\033[0;32m = \033[33m" << x << "\033[0m\n";}
template<typename T, typename... Args> void dbg_out(string s, T x, Args... args) {for (int i=0, b=0; i<(int)s.size(); i++) if (s[i] == '(' || s[i] == '{') b++; else
if (s[i] == ')' || s[i] == '}') b--; else if (s[i] == ',' && b == 0) {cerr << "\033[1;35m" << s.substr(0, i) << "\033[0;32m = \033[33m" << x << "\033[31m | "; dbg_out(s.substr(s.find_first_not_of(' ', i + 1)), args...); break;}}
#ifdef LOCAL
#define dbg(...) dbg_out(#__VA_ARGS__, __VA_ARGS__)
#else
#define dbg(...)
#endif

#define ar array
#define ll long long
#define ld long double
#define sz(x) ((int)x.size())
#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++) 
#define all(a) (a).begin(), (a).end()

const int MAX_N = 1e5 + 5;
const int MAX_L = 20;
const int MAX_C = 26;
const ll MOD = 1e9 + 7;
const ll INF = 1e9;
const ld EPS = 1e-9;

template<int _MOD> struct Modular {
    int v; explicit operator int() const { return v; } // explicit -> don't silently convert to int
    Modular() { v = 0; }
    Modular(ll _v) { v = int((-_MOD < _v && _v < _MOD) ? _v : _v % _MOD); if (v < 0) v += _MOD; }
    friend std::ostream& operator<<(std::ostream& out, const Modular& n) { return out << int(n); }
    friend std::istream& operator>>(std::istream& in, Modular& n) { ll v_; in >> v_; n = Modular(v_); return in; }
    friend bool operator==(const Modular& a, const Modular& b) { return a.v == b.v; }
    friend bool operator!=(const Modular& a, const Modular& b) { return a.v != b.v; }
    friend bool operator<(const Modular& a, const Modular& b) { return a.v < b.v; }
    Modular& operator+=(const Modular& m) { if ((v += m.v) >= _MOD) v -= _MOD; return *this; }
    Modular& operator-=(const Modular& m) { if ((v -= m.v) < 0) v += _MOD; return *this; }
    Modular& operator*=(const Modular& m) { v = int((ll)v*m.v%_MOD); return *this; }
    Modular& operator/=(const Modular& m) { return (*this) *= inverse(m); }
    Modular operator-() const { return Modular(-v); }
    Modular& operator++() { return *this += 1; }
    Modular& operator--() { return *this -= 1; }
    friend Modular power(Modular a, ll p) {
        Modular ans = 1; assert(p >= 0);
        for (; p; p /= 2, a *= a) if (p&1) ans *= a;
        return ans; 
    }
    friend Modular inverse(const Modular& a) { assert(a.v != 0); return power(a, _MOD-2); }
    friend Modular operator+(Modular a, const Modular& b) { return a += b; }
    friend Modular operator-(Modular a, const Modular& b) { return a -= b; }
    friend Modular operator*(Modular a, const Modular& b) { return a *= b; }
    friend Modular operator/(Modular a, const Modular& b) { return a /= b; }
    friend Modular operator++(Modular& a, int) { Modular r = a; ++a; return r; }friend Modular operator--(Modular& a, int) { Modular r = a; --a; return r; }
};

using mint = Modular<MOD>;
using mint2 = Modular<MOD - 1>;
 
void solve(int tc = 0) {
    int n; cin >> n;
    vector<pair<mint,ll>> a(n);
    for (auto &[p, k] : a) cin >> p >> k;
    mint num = 1, sum = 1, mul = 1;
    mint2 tmp = 1;
    for (auto [p, k] : a) {
        num *= (k + 1);
        sum *= (power(p, k + 1) - 1) / (p - 1);
        mul = power(mul, k + 1) * power(power(p, k * (k + 1) / 2), int(tmp));
        tmp *= (k + 1);
    }
    cout << num << " " << sum << " " << mul << "\n";
}

signed main() {
    ios_base::sync_with_stdio(false); cin.tie(NULL);
    int tc = 1;
    // cin >> tc;
    for (int t = 1; t <= tc; t++) {
        // cout << "Case #" << t << ": ";
        solve(t);
    }
}