#pragma GCC optimize("Ofast") #pragma GCC target("avx2,bmi2,popcnt,lzcnt") #include #include #include #include #include #include class strictInput { char *p; off_t cur = 0; off_t len = 0; public: explicit strictInput(int fd = 0) { struct stat st; fstat(fd, &st); p = (char *)mmap(NULL, st.st_size, PROT_READ, MAP_SHARED, fd, 0); len = st.st_size; } char readChar() { assert(cur != len); return p[cur++]; } void unreadChar() { assert(cur != 0); --cur; } bool isEOF() { return cur == len; } void readEOF() { assert(isEOF()); } void readSpace() { assert(readChar() == ' '); } void readEoln() { assert(readChar() == '\n'); } // reads uint64_t in range [from, to] uint64_t readU64(uint64_t from = 0, uint64_t to = UINT64_MAX) { uint64_t cur = 0; off_t read_cnt = 0; bool leading_zero = false; while (!isEOF()) { char p = readChar(); if (!('0' <= p && p <= '9')) { unreadChar(); break; } uint64_t v = p - '0'; assert(cur <= UINT64_MAX / 10); cur *= 10; assert(cur <= UINT64_MAX - v); cur += v; if (read_cnt == 0 && v == 0) leading_zero = true; ++read_cnt; } if (cur == 0) assert(read_cnt == 1); else assert(!leading_zero); assert(from <= cur && cur <= to); return cur; } // reads int64_t in range [from, to] int64_t readI64(int64_t from = INT64_MIN, int64_t to = INT64_MAX) { uint64_t cur = 0; off_t read_cnt = 0; bool leading_zero = false; bool leading_minus = readChar() == '-'; if (!leading_minus) unreadChar(); while (!isEOF()) { char p = readChar(); if (!('0' <= p && p <= '9')) { unreadChar(); break; } uint64_t v = p - '0'; assert(cur <= UINT64_MAX / 10); cur *= 10; assert(cur <= UINT64_MAX - v); cur += v; if (read_cnt == 0 && v == 0) leading_zero = true; ++read_cnt; } if (cur == 0) assert(read_cnt == 1 && !leading_minus); else assert(!leading_zero); if (cur <= INT64_MAX) { int64_t ret = cur; if (leading_minus) ret = -ret; assert(from <= ret && ret <= to); return ret; } else { assert(leading_minus && cur == uint64_t(INT64_MIN)); assert(from == INT64_MIN); return INT64_MIN; } } }; #include #include #include #include #include using namespace std; int main() { strictInput Inp; int N; N = Inp.readI64(1, 100'000); Inp.readEoln(); vector> V; for (int i = 0; i < N; ++i) { int a, b; a = Inp.readI64(-1'000'000'000, 1'000'000'000); Inp.readSpace(); b = Inp.readI64(-1'000'000'000, 1'000'000'000); Inp.readEoln(); if (a == 0 && b == 0) continue; if (a < 0) a = -a, b = -b; V.emplace_back(a, b); } Inp.readEOF(); sort(V.begin(), V.end(), [&](auto a, auto b) { return (long long)a.first * b.second > (long long)b.first * a.second; }); long long x = 0, y = 0; __int128 ans = 1; for (auto [dx, dy] : V) { ans += (__int128)x * dy - (__int128)y * dx; ans += gcd(dx, dy); x += dx; y += dy; } const int MOD = 1'000'000'007; int ret = ans % MOD; if (ret < 0) ret += MOD; cout << ret << endl; }