#include using namespace std; using VS = vector; using LL = long long; using VI = vector; using VVI = vector; using PII = pair; using PLL = pair; using VL = vector; using VVL = vector; #define ALL(a) begin((a)),end((a)) #define RALL(a) (a).rbegin(), (a).rend() #define SZ(a) int((a).size()) #define SORT(c) sort(ALL((c))) #define RSORT(c) sort(RALL((c))) #define UNIQ(c) (c).erase(unique(ALL((c))), end((c))) #define FOR(i, s, e) for (int(i) = (s); (i) < (e); (i)++) #define FORR(i, s, e) for (int(i) = (s); (i) > (e); (i)--) #define debug(x) cerr << #x << ": " << x << endl const int INF = 1e9; const LL LINF = 1e16; const LL MOD = 1000000007; const double PI = acos(-1.0); int DX[8] = { 0, 0, 1, -1, 1, 1, -1, -1 }; int DY[8] = { 1, -1, 0, 0, 1, -1, 1, -1 }; /* ----- 2018/07/30 Problem: yukicoder 187 / Link: http://yukicoder.me/problems/no/187 ----- */ /* ------問題------ 諸外国では,○+□=8のように,答えがたくさんある問題があるようですが,採点が大変ですよね. 今度は,中華風にアレンジしてみましょう. N 個の整数の 2 つ組 (X1,Y1),(X2,Y2),…,(XN,YN) が与えられるので,   □ mod Yk=Xk,k=1,2,…,N を同時に満たす□に当てはまる正整数を求めてください. あれ,これは,答えがたくさんあるかもしれません. その場合は,最も小さいものを求めてください. 最も小さいものでも大きい数になるかもしれないので,答えを 109+7 で割った余りだけ答えてください. -----問題ここまで----- */ /* -----解説等----- 100%写経 記事ありがとうございます(https://qiita.com/drken/items/ae02240cd1f8edfc86fd) ----解説ここまで---- */ long long GCD(long long a, long long b) { if (b == 0) return a; else return GCD(b, a % b); } long long PreGarner(vector &b, vector &m, long long MOD) { long long res = 1; for (int i = 0; i < (int)b.size(); ++i) { for (int j = 0; j < i; ++j) { long long g = GCD(m[i], m[j]); if ((b[i] - b[j]) % g != 0) return -1; m[i] /= g; m[j] /= g; long long gi = GCD(m[i], g), gj = g / gi; do { g = GCD(gi, gj); gi *= g, gj /= g; } while (g != 1); m[i] *= gi, m[j] *= gj; b[i] %= m[i], b[j] %= m[j]; } } for (int i = 0; i < (int)b.size(); ++i) (res *= m[i]) %= MOD; return res; } inline long long add(long long a, long long m) { long long res = a % m; if (res < 0) res += m; return res; } long long extGCD(long long a, long long b, long long &p, long long &q) { if (b == 0) { p = 1; q = 0; return a; } long long d = extGCD(b, a%b, q, p); q -= a / b * p; return d; } long long modinv(long long a, long long m) { long long x, y; extGCD(a, m, x, y); return add(x, m); } long long Garner(vector b, vector m, long long MOD) { m.push_back(MOD); vector coeffs((int)m.size(), 1); vector constants((int)m.size(), 0); for (int k = 0; k < (int)b.size(); ++k) { long long t = add((b[k] - constants[k]) * modinv(coeffs[k], m[k]), m[k]); for (int i = k + 1; i < (int)m.size(); ++i) { (constants[i] += t * coeffs[i]) %= m[i]; (coeffs[i] *= m[k]) %= m[i]; } } return constants.back(); } int main() { cin.tie(0); ios_base::sync_with_stdio(false); int N; cin >> N; int f = 0; VL x(N), y(N); FOR(i, 0, N) { cin >> x[i] >> y[i]; if (x[i])f = 1; } LL lcms = PreGarner(x, y, MOD); LL ans; if (!f)ans = lcms;// 0 else if (lcms == -1)ans = -1; else ans = Garner(x,y,MOD); cout << ans << "\n"; return 0; }