/*** author: yuji9511 ***/ #include // #include // using namespace atcoder; using namespace std; using ll = long long; using lpair = pair; using vll = vector; const ll MOD = 1e9+7; const ll INF = 1e18; #define rep(i,m,n) for(ll i=(m);i<(n);i++) #define rrep(i,m,n) for(ll i=(m);i>=(n);i--) #define printa(x,n) for(ll i=0;i void print(H&& h, T&&... t){cout<(t)...);} constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } constexpr std::pair inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b 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; // |m1 * u| <= |m1| * s <= b // [3]: // (s - t * u) * |m1| + t * |m0 - m1 * u| // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u) // = s * |m1| + t * |m0| <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if (m0 < 0) m0 += b / s; return {s, m0}; } std::pair crt(const std::vector& r, const std::vector& m) { assert(r.size() == m.size()); int n = int(r.size()); // Contracts: 0 <= r0 < m0 long long r0 = 0, m0 = 1; for (int i = 0; i < n; i++) { assert(1 <= m[i]); long long r1 = safe_mod(r[i], m[i]), m1 = m[i]; if (m0 < m1) { std::swap(r0, r1); std::swap(m0, m1); } if (m0 % m1 == 0) { if (r0 % m1 != r1) return {0, 0}; continue; } // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1) // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1)); // r2 % m0 = r0 // r2 % m1 = r1 // -> (r0 + x*m0) % m1 = r1 // -> x*u0*g % (u1*g) = (r1 - r0) (u0*g = m0, u1*g = m1) // -> x = (r1 - r0) / g * inv(u0) (mod u1) // im = inv(u0) (mod u1) (0 <= im < u1) long long g, im; std::tie(g, im) = inv_gcd(m0, m1); long long u1 = (m1 / g); // |r1 - r0| < (m0 + m1) <= lcm(m0, m1) if ((r1 - r0) % g) return {0, 0}; // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1) long long x = (r1 - r0) / g % u1 * im % u1; // |r0| + |m0 * x| // < m0 + m0 * (u1 - 1) // = m0 + m0 * m1 / g - m0 // = lcm(m0, m1) r0 += x * m0; m0 *= u1; // -> lcm(m0, m1) if (r0 < 0) r0 += m0; } return {r0, m0}; } void solve(){ ll N; cin >> N; vll r(N),c(N); rep(i,0,N){ cin >> r[i] >> c[i]; } auto res = crt(r,c); if(res.first == 0){ print(-1); }else{ print(res.first % MOD); } // ll a[35]; // rep(i,2,31) cin >> a[i]; // vll r, c; // rep(i,2,31){ // r.push_back(a[i] % (i-1)); // c.push_back(i-1); // } // auto res = crt(r,c); // if(res.first == 0 || res.first > (ll)1e12){ // print("invalid"); // }else{ // bool ok = true; // rep(i,2,31){ // ll num = 0; // ll n = res.first; // while(n > 0){ // num += n % i; // n /= i; // } // if(num != a[i]) ok = false; // } // print(res.second); // if(ok){ // print(res.first); // }else{ // print("invalid"); // } // } } int main(){ cin.tie(0); ios::sync_with_stdio(false); solve(); }