#include #define ll long long #define INF 1000000005 #define MOD 1000000007 #define EPS 1e-10 #define rep(i,n) for(int i=0;i<(int)n;++i) #define each(a, b) for(auto (a): (b)) #define all(v) (v).begin(),(v).end() #define fi first #define se second #define pb push_back #define show(x) cout <<#x<<" = "<<(x)<P; const int MAX_N = 100005; ll mod_pow(ll a,ll b) { a %= MOD; ll res = 1; while(b){ if(b & 1){ res = res * a % MOD; } a = a * a %MOD; b >>= 1; } return res; } ll pow_string(ll a,string& s) { ll nw = 1; rep(i,s.length()){ int val = s[i]-'0'; nw = mod_pow(nw,10); nw = nw*mod_pow(a,val)%MOD; } return nw; } template class mat : public vector > { private: int r,c; //行,列 public: int row() const { return r; } int column() const { return c; } mat(int n,int m,T val = 0){ this->r = n,this->c = m; rep(i,n){ this->push_back(vector(m,val)); } } mat operator+(const mat& another){ if(this->r != another.r && this->c != another.c){ cout << "足し算失敗(サイズ不一致)" << endl; exit(1); } mat X(this->r,this->c); rep(i,this->r){ rep(j,this->c){ X[i][j] = (*this)[i][j] + another[i][j]; } } return X; } mat operator+(const T val){ mat X(this->r,this->c); rep(i,this->r){ rep(j,this->c){ X[i][j] = (*this)[i][j] + val; } } return X; } mat operator-(const mat& another){ if(this->r != another.r && this->c != another.c){ cout << "引き算失敗(サイズ不一致)" << endl; exit(1); } mat X(this->r,this->c); rep(i,this->r){ rep(j,this->c){ X[i][j] = (*this)[i][j] - another[i][j]; } } return X; } mat operator-(const T val){ mat X(this->r,this->c); rep(i,this->r){ rep(j,this->c){ X[i][j] = (*this)[i][j] - val; } } return X; } vector operator*(const vector& another){ if(this->c != another.size()){ cout << "掛け算失敗(サイズ不一致)" << endl; exit(1); } vector vec(this->r,0); rep(i,this->r){ rep(j,this->c){ vec[i] += (*this)[i][j] * another[j]; } } return vec; } mat operator*(const mat& another){ if(this->c != another.r){ cout << "掛け算失敗(サイズ不一致)" << endl; exit(1); } mat X(this->r,another.c); rep(i,this->r){ rep(k,this->c){ rep(j,another.c){ X[i][j] += (*this)[i][k]*another[k][j]; } } } return X; } mat operator-(){ mat X(this->r,this->c); rep(i,this->r){ rep(j,this->c){ X[i][j] = -(*this)[i][j]; } } return X; } int rank(){ int n = this->r; int res = 0; mat B(n,n); rep(i,n){ rep(j,n){ B[i][j] = (*this)[i][j]; } } rep(i,n){ int pivot = i; for(int j=i;j abs(B[pivot][i])){ pivot = j; } } if(abs(B[pivot][i]) < EPS){ continue; } swap(B[i],B[pivot]); for(int j=i+1;jr != this->c){ cout << "正方行列でない(行列式定義不可)" << endl; exit(1); } T ans = 1; int n = this->r; mat B(n,n); rep(i,n){ rep(j,n){ B[i][j] = (*this)[i][j]; } } rep(i,n) { for(int j=i+1;jr != this->c){ cout << "正方行列でない(逆行列定義不可)" << endl; exit(1); } int n = this->r; mat B(n,2*n); rep(i,n){ rep(j,n){ B[i][j] = (*this)[i][j]; } } rep(i,n){ B[i][n+i] = 1; } rep(i,n){ int pivot = i; for(int j=i;j abs(B[pivot][i])){ pivot = j; } } if(abs(B[pivot][i]) < EPS){ cout << "解なしor不定" << endl; exit(1); } swap(B[i],B[pivot]); for(int j=i+1;j<=2*n;j++){ B[i][j] /= B[i][i]; } rep(j,n){ if(i != j){ for(int k=i+1;k<=2*n;k++){ B[j][k] -= B[j][i] * B[i][k]; } } } } mat res(n,n); rep(i,n){ rep(j,n){ res[i][j] = B[i][n+j]; } } return res; } void print(){ rep(i,this->r){ rep(j,(this->c)-1){ cout << (*this)[i][j] << ","; } cout << (*this)[i][(this->c)-1] << endl; } } }; template vector eq_solve(const mat& A,const vector& b){ if(A.row() != A.column()){ cout << "正方行列でない(解なしor不定)" << endl; exit(1); } int n = A.row(); mat B(n,n+1); rep(i,n){ rep(j,n){ B[i][j] = A[i][j]; } } rep(i,n){ B[i][n] = b[i]; } rep(i,n){ int pivot = i; for(int j=i;j abs(B[pivot][i])){ pivot = j; } } if(abs(B[pivot][i]) < EPS){ cout << "解なしor不定" << endl; exit(1); } swap(B[i],B[pivot]); for(int j=i+1;j<=n;j++){ B[i][j] /= B[i][i]; } rep(j,n){ if(i != j){ for(int k=i+1;k<=n;k++){ B[j][k] -= B[j][i] * B[i][k]; } } } } vector res(n); rep(i,n){ res[i] = B[i][n]; } return res; } template mat pow(mat A,ll cnt) { if(A.row() != A.column()){ cout << "累乗不可" << endl; } int n = A.row(); mat B(n,n); rep(i,n){ B[i][i] = 1; } while(cnt>0){ if(cnt & 1){ B = B*A; } A = A*A; cnt >>= 1; } return B; } template mat mod_mul(mat& A,mat& B) { if(A.column() != B.row()){ cout << "掛け算失敗(サイズ不一致)" << endl; exit(1); } mat X(A.row(),B.column()); rep(i,A.row()){ rep(k,A.column()){ rep(j,B.column()){ X[i][j] = (X[i][j] + A[i][k]*B[k][j]) % MOD; } } } return X; } template mat mod_pow(mat A,ll cnt) { if(A.row() != A.column()){ cout << "累乗不可" << endl; } int n = A.row(); mat B(n,n); rep(i,n){ B[i][i] = 1; } while(cnt>0){ if(cnt & 1){ B = mod_mul(B,A); } A = mod_mul(A,A); cnt >>= 1; } return B; } int main() { int n; cin >> n; ll ans = 1; mat a(2,2); a[0][1] = 1,a[1][0] = 1,a[1][1] = 1; vector vec(2); vec[0] = 1,vec[1] = 2; rep(i,n){ ll num; string s; cin >> num >> s; ll tt; mat b = pow(a,num-1); vector res = b*vec; tt = res[1] % MOD; ll t = pow_string(tt,s); ans = ans*t % MOD; } cout << ans << endl; return 0; }