#line 1 "a.cpp" #pragma GCC optimize("O3") #pragma GCC target("avx2") #pragma GCC optimize("unroll-loops") #include #if __has_include() using int1024_t = long long; #else #include using namespace boost::multiprecision; #endif using namespace std; #line 2 "/home/yuruhiya/programming/library/Math/Matrix.cpp" #include #include using namespace std; template struct Matrix { size_t h, w; vector> A; public: static Matrix I(size_t n) { Matrix A(n); for (size_t i = 0; i < n; ++i) { A[i][i] = 1; } return A; } Matrix() {} Matrix(size_t _h, size_t _w) : h(_h), w(_w), A(h, vector(w, 0)) {} Matrix(size_t _h) : h(_h), w(_h), A(h, vector(w, 0)){}; Matrix(const vector>& _A) : h(_A.size()), w(_A[0].size()), A(_A) {} size_t height() const { return h; } size_t width() const { return w; } const vector& operator[](int i) const { return A[i]; } vector& operator[](int i) { return A[i]; } const vector>& operator*() const { return A; } Matrix& operator+=(const Matrix& B) { assert(h == B.height() && w == B.width()); for (size_t i = 0; i < h; ++i) { for (size_t j = 0; j < w; ++j) { A[i][j] += B[i][j]; } } return *this; } Matrix& operator-=(const Matrix& B) { assert(h == B.height() && w == B.width()); for (size_t i = 0; i < h; ++i) { for (size_t j = 0; j < w; ++j) { A[i][j] -= B[i][j]; } } return *this; } Matrix& operator*=(const Matrix& B) { size_t n = B.width(); assert(w == B.height()); vector> C(h, vector(n, 0)); for (size_t i = 0; i < h; i++) { for (size_t j = 0; j < n; j++) { for (size_t k = 0; k < w; k++) { C[i][j] += A[i][k] * B[k][j]; } } } A.swap(C); return *this; } Matrix& operator^=(long long k) { Matrix B = Matrix::I(h); while (k > 0) { if (k & 1) { B *= *this; } *this *= *this; k >>= 1; } A.swap(B.A); return *this; } Matrix operator+(const Matrix& B) const { return Matrix(*this) += B; } Matrix operator-(const Matrix& B) const { return Matrix(*this) -= B; } Matrix operator*(const Matrix& B) const { return Matrix(*this) *= B; } Matrix operator^(const long long k) const { return Matrix(*this) ^= k; } Matrix pow(long long k) const { return *this ^ k; } }; #line 4 "/home/yuruhiya/programming/library/Math/Fibonacci.cpp" using namespace std; template value_type Fibonacci(long long n) { Matrix A(vector>{{1, 1}, {1, 0}}); Matrix B(vector>{{1}, {0}}); return (A.pow(n) * B)[1][0]; } #line 4 "/home/yuruhiya/programming/library/Math/modint.cpp" #include using namespace std; template struct modint { using T = long long; T n; constexpr modint(const T x = 0) : n(x % MOD) { if (n < 0) n += MOD; } constexpr int get_mod() const { return MOD; } constexpr modint operator+() const { return *this; } constexpr modint operator-() const { return n ? MOD - n : 0; } constexpr modint& operator++() { if (MOD <= ++n) n = 0; return *this; } constexpr modint& operator--() { if (n <= 0) n = MOD; n--; return *this; } constexpr modint operator++(int) { modint t = *this; ++*this; return t; } constexpr modint operator--(int) { modint t = *this; --*this; return t; } constexpr modint next() const { return ++modint(*this); } constexpr modint pred() const { return --modint(*this); } constexpr modint operator+(const modint& m) const { return modint(*this) += m; } constexpr modint operator-(const modint& m) const { return modint(*this) -= m; } constexpr modint operator*(const modint& m) const { return modint(*this) *= m; } constexpr modint operator/(const modint& m) const { return modint(*this) /= m; } constexpr modint& operator+=(const modint& m) { n += m.n; if (n >= MOD) n -= MOD; return *this; } constexpr modint& operator-=(const modint& m) { n -= m.n; if (n < 0) n += MOD; return *this; } constexpr modint& operator*=(const modint& m) { n = n * m.n % MOD; return *this; } constexpr modint& operator/=(const modint& m) { T a = m.n, b = MOD, u = 1, v = 0; while (b) { T t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } n = n * u % MOD; if (n < 0) n += MOD; return *this; } constexpr bool operator==(const modint& m) const { return n == m.n; } constexpr bool operator!=(const modint& m) const { return n != m.n; } template constexpr modint pow(M m) const { if (0 <= m) { modint t = n, res = 1; while (m > 0) { if (m & 1) res *= t; t *= t; m >>= 1; } return res; } else { return (modint(1) / n).pow(-m); } } template constexpr modint operator^(M m) const { return pow(m); } friend ostream& operator<<(ostream& os, const modint& m) { return os << m.n; } friend istream& operator>>(istream& is, modint& m) { long long x; cin >> x; m = modint(x); return is; } }; using mint = modint<1000000007>; using VM = vector; inline mint operator""_m(unsigned long long n) { return n; } #line 14 "a.cpp" mint pow_mod(mint a, int1024_t b) { mint res = 1, k = a; while (b > 0) { if (b % 2 == 1) res *= k; k *= k; b /= 2; } return res; } int main() { cin.tie(nullptr); ios_base::sync_with_stdio(false); mint ans = 1; int n; cin >> n; while (n--) { long long a; int1024_t b; cin >> a >> b; ans *= pow_mod(Fibonacci(a + 2), b); } cout << ans << endl; }