#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; typedef double ld; typedef pair LDP; const ld eps = 1e-12; const ld pi = acos(-1.0); ll mod_pow(ll x, ll n, ll m = mod) { ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n % mod + mod) % mod; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } const int max_n = 1 << 20; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } ll gcd(ll a, ll b) { if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } //x,yがax+by=gcd(a,b)の解になる ll extgcd(ll a, ll b, ll& x, ll& y) { ll d = a; if (b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else { x = 1; y = 0; } return d; } //aのmod mでの逆元を求める ll mod_inverse(ll a, ll m) { ll x, y; extgcd(a, m, x, y); return (m + x % m) % m; } bool isp[40000]; vector ps; void init() { fill(isp + 2, isp + 40000, true); for (int i = 2; i * i <= 1000000000; i++) { if (!isp[i])continue; ps.push_back(i); for (int j = 2 * i; j < 40000; j += i) { isp[j] = false; } } } void solve() { int n; cin >> n; vector> vs; rep(i, n) { int x, y; cin >> x >> y; int cop = y; for (int p : ps) { if (cop % p == 0) { int cnt = 0; int s = 1; while (cop % p == 0) { cnt++; cop /= p; s *= p; } vs.push_back({ {p,cnt},x % s }); } } if (cop > 1) { vs.push_back({ {cop,1},x % cop }); } } sort(all(vs)); vector

vr; vr.push_back({ 1,0 }); rep(i, vs.size()) { int le = i; while (i + 1 < vs.size() && vs[i].first.first == vs[i + 1].first.first) { i++; } for (int j = le + 1; j <= i; j++) { int dif = vs[j].first.second - vs[j - 1].first.second; if (dif == 0) { if (vs[j].second != vs[j - 1].second) { cout << -1 << "\n"; return; } } else { int x = 1; rep(k, dif)x *= vs[j].first.first; int r = vs[j].second - vs[j - 1].second; if (r % x) { cout << -1 << "\n"; return; } } } int x = 1; rep(k, vs[i].first.second)x *= vs[i].first.first; vr.push_back({ x,vs[i].second }); } sort(all(vr)); int len = vr.size(); vector memo(len); memo[0] = vr[1].second; //rep(i, len)cout << vr[i].first << " " << vr[i].second << "\n"; for (int i = 1; i < len-1; i++) { //memo[i] ll s = 0; for (int j = 0; j < i; j++) { s = (s + memo[j] * vr[j].first) % vr[i+1].first; } //cout << "? " << i << " " << s << "\n"; memo[i] = vr[i + 1].second - s; if (memo[i] < 0)memo[i] += vr[i + 1].first; //cout << z << "\n"; rep(j, i+1) { memo[i] = memo[i] * mod_inverse(vr[j].first, vr[i + 1].first) % vr[i + 1].first; } } //rep(i, len - 1)cout << memo[i] << "\n"; ll ans = 0; ll z = 1; for (int i = 0; i < len-1; i++) { z = z * vr[i].first % mod; ans = (ans + memo[i] * z) % mod; } cout << ans << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(10); //init_f(); init(); //expr(); //int t; cin >> t; rep(i, t) solve(); return 0; }