#include #define int long long #define pii pair #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define REP(i,n) FOR(i,0,n) #define ALL(c) (c).begin(),(c).end() #define ZERO(a) memset(a,0,sizeof(a)) #define MINUS(a) memset(a,0xff,sizeof(a)) #define MINF(a) memset(a,0x3f,sizeof(a)) #define POW(n) (1LL<<(n)) #define IN(i,a,b) (a <= i && i <= b) using namespace std; template inline bool CHMIN(T& a,T b) { if(a>b) { a=b; return 1; } return 0; } template inline bool CHMAX(T& a,T b) { if(a inline void SORT(T& a) { sort(ALL(a)); } template inline void REV(T& a) { reverse(ALL(a)); } template inline void UNI(T& a) { sort(ALL(a)); a.erase(unique(ALL(a)),a.end()); } const int MOD = 1000000007; const int INF = 0x3f3f3f3f3f3f3f3f; const double EPS = 1e-10; /* ---------------------------------------------------------------------------------------------------- */ int gcd(int a, int b) { while (b) { int c = a % b; a = b; b = c; } return a; } // garner のアルゴリズムの前処理 // m_1,m_2,... を互いに素にする // lcm(m_1,m_2,...) を返す int pre_garner(vector &b, vector &m, int mod = MOD) { int res = 1; for (int i = 0; i < (int)b.size(); i++) { for (int j = 0; j < i; j++) { int g = gcd(m[i],m[j]); if ((b[i]-b[j]) % g != 0) return -1; m[i] /= g; m[j] /= g; int 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; } int inv_mod(int a, int mod = MOD) { int b = mod, x = 1, y = 0; while (b) { int t = a/b; a -= t*b; swap(a,b); x -= t*y; swap(x,y); } x %= mod; if (x < 0) x += mod; return x; } // garner のアルゴリズム | (m_i,m_j) は互いに素 int garner(vector b, vector m, int mod = 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++) { int t = ((b[k]-constants[k])*inv_mod(coeffs[k],m[k])%m[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(); } signed main() { cin.tie(0); ios_base::sync_with_stdio(false); cout << fixed << setprecision(10); int N; cin >> N; vector b(N),m(N); bool all_zero = true; REP(i,N) { cin >> b[i] >> m[i]; if (b[i]) all_zero = false; } int l = pre_garner(b,m); if (all_zero) cout << l << endl; else if (l < 0) cout << -1 << endl; else cout << garner(b,m) << endl; return 0; }