#ifndef Modint_hpp #define Modint_hpp #include #include template class modint { int val; public: constexpr modint() noexcept : val{0} {} constexpr modint(long long x) noexcept : val((x %= mod) < 0 ? mod + x : x) {} constexpr long long value() const noexcept { return val; } constexpr modint operator++(int) noexcept { modint t = *this; return ++val, t; } constexpr modint operator--(int) noexcept { modint t = *this; return --val, t; } constexpr modint &operator++() noexcept { return ++val, *this; } constexpr modint &operator--() noexcept { return --val, *this; } constexpr modint operator-() const noexcept { return modint(-val); } constexpr modint &operator+=(const modint &other) noexcept { return (val += other.val) < mod ? 0 : val -= mod, *this; } constexpr modint &operator-=(const modint &other) noexcept { return (val += mod - other.val) < mod ? 0 : val -= mod, *this; } constexpr modint &operator*=(const modint &other) noexcept { return val = (long long)val * other.val % mod, *this; } constexpr modint &operator/=(const modint &other) noexcept { return *this *= inverse(other); } constexpr modint operator+(const modint &other) const noexcept { return modint(*this) += other; } constexpr modint operator-(const modint &other) const noexcept { return modint(*this) -= other; } constexpr modint operator*(const modint &other) const noexcept { return modint(*this) *= other; } constexpr modint operator/(const modint &other) const noexcept { return modint(*this) /= other; } constexpr bool operator==(const modint &other) const noexcept { return val == other.val; } constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; } constexpr bool operator!() const noexcept { return !val; } friend constexpr modint operator+(long long x, modint y) noexcept { return modint(x) + y; } friend constexpr modint operator-(long long x, modint y) noexcept { return modint(x) - y; } friend constexpr modint operator*(long long x, modint y) noexcept { return modint(x) * y; } friend constexpr modint operator/(long long x, modint y) noexcept { return modint(x) / y; } static constexpr modint inverse(const modint &other) noexcept { assert(other != 0); int a{mod}, b{other.val}, u{}, v{1}, t{}; while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v; return {u}; } static constexpr modint pow(modint other, long long e) noexcept { if(e < 0) e = e % (mod - 1) + mod - 1; modint res{1}; while(e) { if(e & 1) res *= other; other *= other, e >>= 1; } return res; } friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; } friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other = {(is >> val, val)}; return is; } }; // class modint template <> class modint<2> { bool val; public: constexpr modint(bool x = false) noexcept : val{x} {} constexpr modint(int x) noexcept : val(x & 1) {} constexpr modint(long long x) noexcept : val(x & 1) {} constexpr operator bool() const noexcept { return val; } constexpr bool value() const noexcept { return val; } constexpr modint &operator+=(const modint &other) noexcept { return val ^= other.val, *this; } constexpr modint &operator-=(const modint &other) noexcept { return val ^= other.val, *this; } constexpr modint &operator*=(const modint &other) noexcept { return val &= other.val, *this; } constexpr modint &operator/=(const modint &other) noexcept { assert(other.val); return *this; } constexpr modint operator!() const noexcept { return !val; } constexpr modint operator-() const noexcept { return *this; } constexpr modint operator+(const modint &other) const noexcept { return val != other.val; } constexpr modint operator-(const modint &other) const noexcept { return val != other.val; } constexpr modint operator*(const modint &other) const noexcept { return val && other.val; } constexpr modint operator/(const modint &other) const noexcept { assert(other.val); return *this; } constexpr bool operator==(const modint &other) const noexcept { return val == other.val; } constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; } friend constexpr modint operator+(long long x, modint y) noexcept { return x & 1 ? !y : y; } friend constexpr modint operator-(long long x, modint y) noexcept { return x & 1 ? !y : y; } friend constexpr modint operator*(long long x, modint y) noexcept { return x & 1 ? y : modint<2>{0}; } friend constexpr modint operator/(long long x, modint y) noexcept { assert(y.val); return x & 1 ? y : modint<2>{0}; } friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; } friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other.val = (is >> val, val & 1); return is; } }; // class modint specialization #endif // Modint_hpp #include namespace std { // hash template size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); } template struct hash> { size_t operator()(pair const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } }; template ::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc::apply(seed, t), get(t)); } }; template struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } }; template struct hash> { size_t operator()(tuple const &t) const { return tuple_hash_calc>::apply(0, t); } }; // iostream template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } template struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis::apply(is, t); return is >> get(t); } }; template struct tupleis { static istream &apply(istream &is, tuple_t &t) { return is; } }; template istream &operator>>(istream &is, tuple &t) { return tupleis, tuple_size>::value - 1>::apply(is, t); } template <> istream &operator>>(istream &is, tuple<> &t) { return is; } template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos::apply(os, t); return os << ' ' << get(t); } }; template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } }; template ostream &operator<<(ostream &os, const tuple &t) { return tupleos, tuple_size>::value - 1>::apply(os, t); } template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; } template , string>::value, nullptr_t> = nullptr> istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; } template , string>::value, nullptr_t> = nullptr> ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; } } // namespace std #ifndef Matrix_hpp #define Matrix_hpp #include #include #include // Field must be a field. template class matrix { size_t h, w; using row_type = std::valarray; using data_type = std::valarray>; data_type data; friend std::istream &operator>>(std::istream &is, matrix &x) { for(size_t i = 0; i != x.h; ++i) { for(size_t j = 0; j != x.w; ++j) is >> x[i][j]; } return is; } friend std::ostream &operator<<(std::ostream &os, const matrix &x) { for(size_t i = 0; i != x.h; ++i) { if(i) os << "\n"; for(size_t j = 0; j != x.w; ++j) os << (j ? " " : "") << x.data[i][j]; } return os; } friend matrix transpose(const matrix &x) { matrix res(x.w, x.h); for(size_t i = 0; i != x.w; ++i) for(size_t j = 0; j != x.h; ++j) res[i][j] = x.data[j][i]; return res; } friend matrix pow(matrix x, long long n) { assert(x.is_square()); matrix res{identity(x.h)}; while(n) { if(n & 1) res *= x; x *= x, n >>= 1; } return res; } // friend matrix inverse(const matrix &x) // { // assert(x.is_square()); // size_t n = x.height(); // matrix ext_x(x), e(identity(n)), res(n); // for(size_t i = 0; i < n; ++i) ext_x[i].insert(end(ext_x[i]), begin(e[i]), end(e[i])); // ext_x = ext_x.row_canonical_form(); // for(size_t i = 0; i < n; ++i) // { // if(std::vector(begin(ext_x[i]), begin(ext_x[i]) + n) != e[i]) return matrix(); // res[i] = std::vector(begin(ext_x[i]) + n, end(ext_x[i])); // } // return res; // } public: matrix(size_t _n = 0) : h(_n), w(_n) { resize(_n, _n);} matrix(size_t _h, size_t _w) : h(_h), w(_w) { resize(_h, _w); } matrix(const data_type &_data) : h(_data.size()), w(_data.size() ? _data[0].size() : 0), data(_data) {} operator data_type() const { return data; } size_t height() const { return h; } size_t width() const { return w; } bool is_square() const { return h == w; } void resize(size_t h, size_t w, const Field val = Field(0)) { data.resize(h, std::valarray(val, w)); } row_type &operator[](const size_t i) { assert(i < data.size()); return data[i]; } static matrix identity(const size_t n) { data_type data(row_type(n), n); for(size_t i = 0; i != n; ++i) data[i][i] = 1; return data; } matrix operator-() const { return {-data}; } matrix &operator+=(const matrix &other) { data += other.data; return *this; } matrix &operator-=(const matrix &other) { data -= other.data; return *this; } matrix &operator*=(matrix other) { matrix res(h, other.w); other = transpose(other); for(size_t i = 0; i != res.h; ++i) for(size_t j = 0; j != other.h; ++j) res[i][j] = (data[i] * other.data[j]).sum(); return *this = res; } matrix operator+(const matrix &x) const { return matrix(*this) += x; } matrix operator-(const matrix &x) const { return matrix(*this) -= x; } matrix operator*(const matrix &x) const { return matrix(*this) *= x; } std::vector row_canonicalize() { std::vector pivots; for(size_t j = 0, rank = 0; j != w; ++j) { bool ispiv = false; for(size_t i = rank; i != h; ++i) { if(data[i][j] != Field{}) { if(ispiv) { const Field r = -data[i][j]; for(size_t k = j; k != w; ++k) data[i][k] += data[rank][k] * r; } else { swap(data[rank], data[i]); Field r = data[rank][j]; for(size_t k = j; k != w; ++k) data[rank][k] /= r; for(size_t k = 0; k != rank; ++k) { r = -data[k][j]; for(size_t l = j; l != w; ++l) data[k][l] += data[rank][l] * r; } ispiv = true; } } } if(ispiv) { ++rank; pivots.emplace_back(j); } } return pivots; } Field determinant() const { matrix x(*this); assert(is_square()); size_t n = height(); Field res(1); for(size_t j = 0; j < n; ++j) { bool ispiv = false; for(size_t i = j; i < n; ++i) { if(x[i][j] != Field{}) { if(ispiv) { const Field r = -x[i][j]; for(size_t k = j; k < n; ++k) x[i][k] += x[j][k] * r; } else { swap(x[i], x[j]); if(i != j) res = -res; const Field r = x[j][j]; res *= r; for(size_t k = j; k < n; ++k) x[j][k] /= r; ispiv = true; } } } if(!ispiv) return Field(0); } return res; } }; #endif main() { std::ios::sync_with_stdio(false), std::cin.tie(nullptr); using namespace std; using mint=modint<(int)1e9+7>; int n,a,b; cin>>a>>b>>n; matrix c({ {a,b}, {1,0}, }); auto ans{pow(c,n)*transpose(matrix({{1,0}}))}; cout << ans[1][0] << "\n"; }