#include #include using namespace std; using namespace atcoder; const long nPrime = 1000000007; //const long nPrime = 998244353; typedef long long ll; const long long nMod = nPrime; class ModInt { long long x; public: ModInt(long long x=0) : x((x%nMod+nMod)%nMod) {} ModInt operator-() const { return ModInt(-x); } ModInt& operator+=(const ModInt& a) { if ((x += a.x) >= nMod) x -= nMod; return *this; } ModInt& operator-=(const ModInt& a) { if ((x += nMod-a.x) >= nMod) x -= nMod; return *this; } ModInt& operator*=(const ModInt& a) { (x *= a.x) %= nMod; return *this; } ModInt operator+(const ModInt& a) const { ModInt res(*this); return res+=a; } ModInt operator-(const ModInt& a) const { ModInt res(*this); return res-=a; } ModInt operator*(const ModInt& a) const { ModInt res(*this); return res*=a; } ModInt Pow(long long t) const { if (!t) return 1; ModInt a = Pow(t>>1); a *= a; if (t&1) a *= *this; return a; } // for prime nMod ModInt Inv() const { return Pow(nMod-2); } ModInt& operator/=(const ModInt& a) { return (*this) *= a.Inv(); } ModInt operator/(const ModInt& a) const { ModInt res(*this); return res/=a; } friend ostream& operator<<(ostream& os, const ModInt& m){ os << m.x; return os; } }; void MakeTable(vector &viInv, vector &viFctr, vector &viFctrInv, bool bUseFctr = false, const long nTableSize = 1000000){ viInv.resize(nTableSize+1, 1); for(long i = 1; i < nTableSize+1; i++){ viInv[i] /= i; } if(!bUseFctr){ return; } viFctr.resize(nTableSize+1, 1); viFctrInv.resize(nTableSize+1, 1); for(long i = 1; i < nTableSize+1; i++){ viFctr[i] = viFctr[i-1] * i; } viFctrInv[nTableSize] /= viFctr[nTableSize]; for(long i = nTableSize; i >= 1; i--){ viFctrInv[i-1] = viFctrInv[i]*i; } } int main() { long n; cin >> n; ModInt nAns = 1; for(long i = 0; i < n; i++){ long p,e; cin >> p >> e; ModInt pm = p,em = e; ModInt S1 = (em+1); S1 *= ((pm.Pow(e+1)-1)/(pm-1)); ModInt S2 = 1; S2 /= (ModInt(1)-pm); S2 *= ((pm.Pow(e+1)-p)/(pm-1) - em*pm.Pow(e+1)); nAns *= (S1-S2); } cout << nAns <