#include using namespace std; using i64 = int64_t; using vi = vector; using vvi = vector; constexpr i64 MOD = 1e9 + 7; template struct mat { vvi d; mat() { d = vvi(n, vi(n)); } mat(initializer_list> m) { for (auto a: m) { vi row(a.begin(), a.end()); d.emplace_back(row); } assert(n == d.size()); assert(n == d.front().size()); }; mat operator+(const mat rhs) { mat ret; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { ret.d[i][j] = d[i][j] + rhs.d[i][j]; ret.d[i][j] %= MOD; ret.d[i][j] += MOD; ret.d[i][j] %= MOD; } } return ret; } mat operator-(const mat rhs) { mat ret; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { ret.d[i][j] = d[i][j] - rhs.d[i][j]; ret.d[i][j] %= MOD; ret.d[i][j] += MOD; ret.d[i][j] %= MOD; } } return ret; } mat operator*(const mat rhs) { mat ret; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { for (int k = 0; k < n; k++) { ret.d[i][j] += d[i][k] * rhs.d[k][j]; ret.d[i][j] %= MOD; ret.d[i][j] += MOD; ret.d[i][j] %= MOD; } } } return ret; } mat operator*(const i64 k) { mat ret; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { ret.d[i][j] = d[i][j] * k; ret.d[i][j] %= MOD; ret.d[i][j] += MOD; ret.d[i][j] %= MOD; } } return ret; } static mat eye() { mat ret; for (int i = 0; i < n; i++) { ret.d[i][i] = 1; } return ret; } }; template mat pow(mat a, i64 n) { if (n == 0) { return mat::eye(); } if (n % 2 == 0) { mat t = pow(a, n / 2); return t * t; } return a * pow(a, n - 1); } i64 fib(i64 n) { if (n <= 1) return n; mat<2> f{{1, 1}, {1, 0}}; mat<2> res = pow(f, n - 2); return (res.d[0][0] + res.d[0][1]) % MOD; } // 負の数は扱っていない // 宣言するときはconvert関数を使う // 掛け算でFFTをやるので畳み込み後の配列の最大要素を1e13程度にして誤差を小さくしたい // BASELOGを大きくすると桁数が1/BASELOGになる代わりに配列の要素が指数関数的に大きくなる // 掛け算をしないのであれば定数倍早くなるのでBASELOGを大きくするとよい。掛け算をするときは3が精度的に安心 constexpr i64 BASE = 10000000000l; constexpr int BASELOG = 10; struct BigInt { // 掛け算のために本来の最大桁数の2倍必要 vi digit = vi(1 << 8); int size; BigInt(int size = 1, i64 a = 0) : size(size) { digit[0] = a; } BigInt(const BigInt& a) { size = a.size; digit = vi(a.digit); } }; bool operator<(BigInt x, BigInt y) { if (x.size != y.size) { return x.size < y.size; } for (int i = x.size - 1; i >= 0; i--) { if (x.digit[i] != y.digit[i]) { return x.digit[i] < y.digit[i]; } } return false; } bool operator>(BigInt x, BigInt y) { return y < x; } bool operator<=(BigInt x, BigInt y) { return !(y < x); } bool operator>=(BigInt x, BigInt y) { return !(x < y); } bool operator!=(BigInt x, BigInt y) { return x < y || y < x; } bool operator==(BigInt x, BigInt y) { return !(x < y) && !(y < x); } BigInt normal(BigInt x, bool all = false) { if (all) { x.size = int(x.digit.size()) - 1; } for (int i = 0; i < x.size; i++) { while (x.digit[i] < 0) { x.digit[i + 1] -= (-x.digit[i] + BASE - 1) / BASE; x.digit[i] = x.digit[i] % BASE + BASE; } while (x.digit[i] >= BASE) { x.digit[i + 1] += x.digit[i] / BASE; x.digit[i] = x.digit[i] % BASE; } } while (x.digit[x.size]) { x.digit[x.size + 1] = x.digit[x.size] / BASE; x.digit[x.size] = x.digit[x.size] % BASE; x.size++; } while (x.size > 1 && x.digit[x.size - 1] == 0) { x.size--; } return x; } BigInt convert(i64 a) { return normal(BigInt(1, a), true); } BigInt convert(const string& s) { BigInt x; x.size = 0; int i = s.size() % BASELOG; if (i > 0) { i -= BASELOG; } for (; i < int(s.size()); i += BASELOG) { i64 a = 0; for (int j = 0; j < BASELOG; j++) { a = 10 * a + (i + j >= 0 ? s[i + j] - '0' : 0); } x.digit[x.size++] = a; } reverse(x.digit.begin(), x.digit.begin() + x.size); return normal(x); } ostream &operator<<(ostream& os, BigInt x) { os << x.digit[x.size - 1]; for (int i = x.size - 2; i >= 0; i--) { os << setw(BASELOG) << setfill('0') << x.digit[i]; } return os; } istream &operator>>(istream& is, BigInt &x) { string s; is >> s; x = convert(s); return is; } string to_string(BigInt &x) { stringstream ss; ss << x.digit[x.size - 1]; for (int i = x.size - 2; i >= 0; i--) { ss << setw(BASELOG) << setfill('0') << x.digit[i]; } return ss.str(); } BigInt operator+(BigInt x, BigInt y) { if (x.size < y.size) { x.size = y.size; } for (int i = 0; i < y.size; i++) { x.digit[i] += y.digit[i]; } return normal(x); } BigInt operator-(BigInt x, BigInt y) { assert(x >= y); for (int i = 0; i < y.size; i++) { x.digit[i] -= y.digit[i]; } return normal(x); } BigInt operator*(BigInt x, i64 a) { for (int i = 0; i < x.size; i++) { x.digit[i] *= a; } return normal(x); } void fft(vector>& a, bool inv = false) { int n = int(a.size()); if (n == 1) return; vector> even(n / 2), odd(n / 2); for (int i = 0; i < n / 2; i++) { even[i] = a[2 * i]; odd[i] = a[2 * i + 1]; } fft(even, inv); fft(odd, inv); complex omega = polar(1.0, (-2 * inv + 1) * 2 * acos(-1) / n); complex pow_omega = 1.0; for (int i = 0; i < n / 2; i++) { a[i] = even[i] + pow_omega * odd[i]; a[i + n / 2] = even[i] - pow_omega * odd[i]; pow_omega *= omega; } } void conv(vector>& a, vector>& b) { fft(a); fft(b); int n = int(a.size()); for (int i = 0; i < n; i++) { a[i] *= b[i] / complex(n); } fft(a, true); } void conv(vi& a, vi& b) { vector> ac, bc; for (int i = 0; i < a.size(); i++) { ac.push_back(a[i]); bc.push_back(b[i]); } conv(ac, bc); a.resize(ac.size()); for (int i = 0; i < ac.size(); i++) { a[i] = long(real(ac[i]) + 0.5); } } BigInt operator*(BigInt x, BigInt y) { conv(x.digit, y.digit); return normal(x, true); } pair divmod(BigInt x, i64 a) { i64 c = 0, t; for (int i = x.size - 1; i >= 0; i--) { t = BASE * c + x.digit[i]; x.digit[i] = t / a; c = t % a; } return pair(normal(x), c); } BigInt operator/(BigInt x, i64 a) { return divmod(x, a).first; } i64 operator%(BigInt x, i64 a) { return divmod(x, a).second; } i64 modpow(i64 a, i64 n, i64 mod) { if (n == 0) return 1; if (n % 2 == 0) { i64 t = modpow(a, n / 2, mod); return t * t % mod; } return a % mod * modpow(a, n - 1, mod) % mod; } int main() { int n; cin >> n; i64 ans = 1; for (int i = 0; i < n; i++) { i64 c; string D; cin >> c >> D; i64 d = convert(D) % MOD; ans *= modpow(fib(c + 2), d, MOD); ans %= MOD; } cout << ans << endl; }