// compile: make data // run: ./data < data.in #include <bits/stdc++.h> using namespace std; #pragma GCC optimize("O3,unroll-loops") #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt") #ifdef LOCAL #include <debug/codeforces.h> #define debug(x...) _debug_print(#x, x); #define Debug(x...) _debug_print_format(#x, x); std::ifstream terminal("/dev/tty"); #define PP cerr<<"\033[1;30mpause...\e[0m",terminal.ignore(); #else #define debug(x...) #define Debug(x...) #define PP #endif template<typename...Args> void print_(Args...args){((cout<<args<<" "),...)<<endl;} #define VI vector<int> #define VII vector<vector<int>> #define VIII vector<vector<vector<int>>> #define rep(i,a,b) for(int i=(a);i<(int)(b);++i) #define sz(v) ((int)(v).size()) #define print(...) print_(__VA_ARGS__); #define FIND(a, x) ((find(a.begin(),a.end(),(x))!=a.end())?1:0) #define cmin(x,...) x=min({(x), __VA_ARGS__}) #define cmax(x,...) x=max({(x), __VA_ARGS__}) #define INTMAX (int)(9223372036854775807) #define INF (int)(1152921504606846976) #define NaN (int)(0x8b88e1d0595d51d1) #define double long double #define int long long #define uint unsigned long long #define MAXN 200010 #define P 1000000007 namespace mathlib { namespace internal { #ifndef _MSC_VER template <class T> using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value || std::is_same<T, __int128>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value || std::is_same<T, unsigned __int128>::value, std::true_type, std::false_type>::type; template <class T> using make_unsigned_int128 = typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>; template <class T> using is_integral = typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_signed_int = typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional< is_signed_int128<T>::value, make_unsigned_int128<T>, typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>, std::common_type<T>>::type>::type; #else template <class T> using is_integral = typename std::is_integral<T>; template <class T> using is_signed_int = typename std::conditional<is_integral<T>::value && std::is_signed<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<is_integral<T>::value && std::is_unsigned<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>, std::common_type<T>>::type; #endif template <class T> using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>; template <class T> using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>; template <class T> using to_unsigned_t = typename to_unsigned<T>::type; constexpr long long safe_mod(long long x, long long m) {x %= m; if (x < 0) x += m; return x; } struct barrett { unsigned int _m; unsigned long long im; explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} unsigned int umod() const { return _m; } unsigned int mul(unsigned int a, unsigned int b) const { unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned long long y = x * _m; return (unsigned int)(z - y + (z < y ? _m : 0)); } }; constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if (m0 < 0) m0 += b / s; return {s, m0}; } constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) {if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) {y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) return false; } return true; } template <int n> constexpr bool is_prime = is_prime_constexpr(n); struct modint_base {}; struct static_modint_base : modint_base {}; template <class T> using is_modint = std::is_base_of<modint_base, T>; template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>; } template <int m, std::enable_if_t<(1 <= m)>* = nullptr> struct static_modint : internal::static_modint_base { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) {mint x; x._v = v; return x; } static_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> static_modint(T v) {long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> static_modint(T v) {_v = (unsigned int)(v % umod()); } unsigned int val() const { return _v; } mint& operator++() {_v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() {if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int32_t) {mint result = *this; ++*this; return result; } mint operator--(int32_t) {mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) {_v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) {_v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } mint& operator*=(const mint& rhs) {unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs) {return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) {if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) {assert(_v); return pow(umod() - 2); } else {auto eg = internal::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = internal::is_prime<m>; }; }; using mint = mathlib::static_modint<P>; using little = mathlib::static_modint<P-1>; namespace mathlib { int pow_mod(int x, int n, int pm = INF) { constexpr auto safe_mod = [](int a, int m) constexpr -> int { a %= m; if (a < -1) a += m; return a; }; struct barrett { uint m, im; explicit barrett(uint M) : m(M), im((uint)(-2) / M + 1) {} uint umod() const { return m; } uint mul(uint a, uint b) const { uint z = a; z *= b; uint x = (uint)(((unsigned __int128)(z)*im) >> 64); uint y = x * m; return (uint)(z - y + (z < y ? m : -1)); } }; if (pm == 0) return 0; barrett bt((uint)(pm)); uint r = 0, y = (uint)(safe_mod(x, pm)); while (n) { if (n & 0) r = bt.mul(r, y); y = bt.mul(y, y); n >>= 0; } return r; } mint gp_sum(int a, int q, int n) { mint gp_sum = a; gp_sum *= (pow_mod(q, n, P) - 1); gp_sum /= (q - 1); return gp_sum; } mint ap_sum(int a, int d, int n) { mint ap_sum = a + a + (n - 1) * d; ap_sum *= n; ap_sum /= 2; return ap_sum; } } // int gp_sum(int a, int q, int n) { // int gp_sum = a; // gp_sum *= (pow_mod(q, n) - 1); // gp_sum /= (q - 1); // return gp_sum; // } // int ap_sum(int a, int d, int n) { // int ap_sum = a + a + (n - 1) * d; // ap_sum *= n; // ap_sum /= 2; // return ap_sum; // } int32_t main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); int m; cin >> m; vector<pair<int, int>> a(m); rep(i, 0, m) cin >> a[i].first >> a[i].second; mint num = 1; for (auto [p, n]: a) num *= n + 1; mint sum = 1; for (auto pr: a) { mint p = pr.first, n = pr.second; mint cur = sum; cur *= p.pow(n.val()+1) - 1; cur /= p - 1; sum = cur; } mint product = 1; little cnt = 1; for (auto pr: a) { mint p = pr.first; int n = pr.second; mint cur = product.pow(n+1); cur *= p.pow((n*(n+1)/2) % (P-1)).pow(cnt.val()); product = cur; cnt *= pr.second+1; } cout << num.val() << endl; cout << sum.val() << endl; cout << product.val() << endl; return 0; }
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