#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) #if defined(_MSC_VER) || __cplusplus > 199711L #define aut(r,v) auto r = (v) #else #define aut(r,v) __typeof(v) r = (v) #endif #define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it) #define all(o) (o).begin(), (o).end() #define pb(x) push_back(x) #define mp(x,y) make_pair((x),(y)) #define mset(m,v) memset(m,v,sizeof(m)) #define INF 0x3f3f3f3f #define INFL 0x3f3f3f3f3f3f3f3fLL using namespace std; typedef vector vi; typedef pair pii; typedef vector > vpii; typedef long long ll; template inline void amin(T &x, U y) { if(y < x) x = y; } template inline void amax(T &x, U y) { if(x < y) x = y; } templateT gcd(T x, T y){if(y==0)return x;else return gcd(y,x%y);} //template typedef int Num; bool reduceLCE(vector > equations, vector > &res) { int n = equations.size(); res.clear(); res.reserve(n); for(int i = 0; i < n; ++ i) { pair p = equations[i]; if(p.first == 1) continue; for(int j = i+1; j < n; ++ j) { pair &q = equations[j]; int g = gcd(p.first, q.first); if((p.second - q.second) % g != 0) { res.clear(); return false; } if(g > 1) { p.first /= g, q.first /= g; for(int h; (h = gcd(p.first, g)) != 1; ) { p.first *= h; g /= h; } q.first *= g; p.second %= p.first; q.second %= q.first; } } res.push_back(p); } return true; } int inverse(signed a, const int MOD) { a %= MOD; if(a < 0) a += MOD; signed b = MOD, u = 1, v = 0; while(b) { signed t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0) u += MOD; return u; } //prefix[i] = CRT(pairs[0..i-1]) mod pairs[i].first を求める // //pairsの一番後ろに(Mod,-1)を追加しておくことによって // CRT(pairs) mod Mod を求めることができる //gcd(pairs[i].first, pairs[j].first) == 1 for i≠j を仮定する //さらに、pairs[i].first > 1 も仮定する! void prefixCRT(const vector > &pairs, vector &prefixes) { int n = pairs.size(); vector ts(n); for(int i = 0; i < n; ++ i) { int m = pairs[i].first, x = 1; for(int j = 0; j < i; ++ j) x = (long long)x * pairs[j].first % m; ts[i] = inverse(x, m); } prefixes.resize(n); for(int i = 0; i < n; ++ i) { int m = pairs[i].first; int n1 = 1, a = 0; for(int j = 0; j < i; ++ j) { int n2 = pairs[j].first, a2 = pairs[j].second; int h = (long long)(a2 - prefixes[j]) * ts[j] % n2; if(h < 0) h += n2; a = (a + (long long)n1 * h) % m; n1 = (long long)n1 * pairs[j].first % m; } prefixes[i] = a; } } int main() { int N; scanf("%d", &N); vector equations; rep(i, N) { int X, Y; cin >> X >> Y; equations.push_back(mp(Y, X)); } vector > pairs; bool ok = reduceLCE(equations, pairs); if(!ok) { puts("-1"); return 0; } const int Mod = 1000000007; pairs.push_back(make_pair(Mod, -1)); vector prefixes; prefixCRT(pairs, prefixes); int ans = prefixes.back(); bool zero = true; rep(i, pairs.size() - 1) zero &= pairs[i].second == 0; if(zero) { int prod = 1; rep(i, pairs.size() - 1) prod = (ll)prod * pairs[i].first % Mod; ans += prod; } printf("%d\n", ans); return 0; }