#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; pair, vector> primes_lpf(const int n) { vector primes; primes.reserve(n / 10); vector lpf(n + 1); for (int i = 2; i <= n; i += 2) lpf[i] = 2; for (int i = 3; i <= n; i += 6) lpf[i] = 3; if (2 <= n) primes.push_back(2); if (3 <= n) primes.push_back(3); // 5 * x <= n, x <= floor(n / 5) const int n5 = n / 5; int x = 5; char add_next = 2; for (; x <= n5; x += add_next, add_next ^= 2 ^ 4) { int px = lpf[x]; if (px == 0) { lpf[x] = px = x; primes.push_back(x); } for (int i = 2;; ++i) { int q = primes[i]; int y = q * x; if (y > n) break; lpf[y] = q; if (q == px) break; } } for (; x <= n; x += add_next, add_next ^= 2 ^ 4) { if (lpf[x] == 0) { lpf[x] = x; primes.push_back(x); } } return {move(primes), move(lpf)}; } constexpr int PSIZE = 10000010; auto [primes, lpf] = primes_lpf(PSIZE); vector>& factorize(int x) { static vector> fs; fs.clear(); while (x != 1) { int p = lpf[x], c = 0; do {x /= p; c++;} while (x % p == 0); fs.emplace_back(p, c); } return fs; } class mint61 { using ull = unsigned long long; using ui128 = __uint128_t; public: static constexpr unsigned long long mod = (1ULL << 61) - 1; ull v = 0; explicit constexpr mint61() {} explicit constexpr mint61(ull x) { v = (x >> 61) + (x & mod); if (v >= mod) v -= mod; } static constexpr mint61 raw(ull x) { mint61 res; res.v = x; return res; } friend constexpr mint61 operator+(mint61 lhs, mint61 rhs) { auto res = lhs.v + rhs.v; return raw(res < mod ? res : res - mod); } friend constexpr mint61 operator-(mint61 lhs, mint61 rhs) { return raw(lhs.v >= rhs.v ? lhs.v - rhs.v : mod + lhs.v - rhs.v); } static constexpr ull multiply_loose_mod(mint61 lhs, mint61 rhs) { // ab = q(m+1)+r = qm+q+r // q+r = ab-qm = ab-floor(ab/(m+1))m < ab-(ab/(m+1)-1)m = ab/(m+1)+m <= (m-1)^2/(m+1)+m = 2m-1-2/(m+1) auto mul = ui128(lhs.v) * rhs.v; return ull(mul >> 61) + ull(mul & mod); } friend constexpr mint61 operator*(mint61 lhs, mint61 rhs) { auto res = multiply_loose_mod(lhs, rhs); return raw(res < mod ? res : res - mod); } mint61& operator+=(mint61 rhs) { return *this = *this + rhs; } mint61& operator-=(mint61 rhs) { return *this = *this - rhs; } mint61& operator*=(mint61 rhs) { return *this = *this * rhs; } friend ostream& operator<<(ostream& os, mint61 x) { return os << x.v; } }; mint61 hsh[10000010]; } int main() { ios::sync_with_stdio(false); static auto RNG = std::mt19937(std::chrono::system_clock::now().time_since_epoch().count()); static auto Distribution = std::uniform_int_distribution(2, mint61::mod - 1); cin.tie(0); rep(i, 10000010) hsh[i] = mint61::raw(Distribution(RNG)); mint61 now, tgt; int k; cin >> k; int p; rep(i, k) { int e; cin >> p >> e; tgt += hsh[p] * mint61::raw(e); } for(int r = 1; r < p; r++) { for(auto [p, c]: factorize(p + 1 - r)) { rrep(_, c) now += hsh[p]; } for(auto [p, c]: factorize(r)) { rrep(_, c) now -= hsh[p]; } if (now.v == tgt.v) { cout << p << ' ' << r << '\n'; return 0; } } cout << -1 << ' ' << -1 << '\n'; }