// May this submission get accepted! #pragma GCC optimize ("O3") #pragma GCC target ("tune=native") #pragma GCC target ("avx") #include // 汎用マクロ #define ALL_OF(x) (x).begin(), (x).end() #define REP(i,n) for (long long i=0, i##_len=(n); i=i##_end; i--) #define UNIQUE(v) do { sort((v).begin(), (v).end()); (v).erase(unique((v).begin(), (v).end()), (v).end()); } while (false) template bool chmax(T &a, const T &b) {if (a < b) {a = b; return true;} return false; } template bool chmin(T &a, const T &b) {if (a > b) {a = b; return true;} return false; } #define INF 0x7FFFFFFF #define LINF 0x7FFFFFFFFFFFFFFFLL #define Yes(q) ((q) ? "Yes" : "No") #define YES(q) ((q) ? "YES" : "NO") #define Possible(q) ((q) ? "Possible" : "Impossible") #define POSSIBLE(q) ((q) ? "POSSIBLE" : "IMPOSSIBLE") #define DUMP(q) cerr << "[DEBUG] " #q ": " << (q) << " at " __FILE__ ":" << __LINE__ << endl #define DUMPALL(q) do { cerr << "[DEBUG] " #q ": ["; REP(i, (q).size()) { cerr << (q)[i] << (i == i_len-1 ? "" : ", "); } cerr << "] at " __FILE__ ":" << __LINE__ << endl; } while (false) template T gcd(const T &a, const T &b) { return a < b ? gcd(b, a) : b ? gcd(b, a % b) : a; } template T lcm(const T &a, const T &b) { return a / gcd(a, b) * b; } // gcc拡張マクロ #define popcount __builtin_popcount #define popcountll __builtin_popcountll // エイリアス #define DANCE_ long #define ROBOT_ unsigned #define HUMAN_ signed #define CHOKUDAI_ const using ll = DANCE_ HUMAN_ DANCE_; using ull = DANCE_ ROBOT_ DANCE_; using cll = DANCE_ DANCE_ CHOKUDAI_; using ld = long double; using namespace std; // モジュール // pdivの余りを取りたくない場合はmatrix::operatorのコメントアウトをいじくれ constexpr ll pdiv = 1000000007LL; // vector> のラッパクラス (プァ~) template class matrix { vector> value; public: T get(const size_t i) const { return this->rows() == 1 ? this->get(0, i) : this->get(i, 0); } T get(const size_t i, const size_t j) const { return this->value.at(i).at(j); } inline size_t rows() const { return this->value.size(); } inline size_t cols() const { return this->value.empty() ? 0 : this->value[0].size(); } matrix() : value() {} matrix(const matrix &a) : value(a.value) {} matrix(size_t n, size_t m = 0) : value(n, vector(m ? m : n, 0)) {} matrix(const vector> &a) : value(a) {} matrix(initializer_list> init) : value() { const size_t n = init.size(); const size_t m = [&]() { size_t maxm = 0; for (const auto& initi : init) { const size_t mi = initi.size(); if (mi > maxm) maxm = mi; } return maxm; }(); this->value = vector>(n, vector(m, 0)); size_t i = 0, j = 0; for (const auto &initi : init) { for (const auto &v : initi) { this->value[i][j++] = v; } i++; j = 0; } } // ラムダ式の引数は(size_t, size_t)、返り値はTとすること (まあ整数型なら大丈夫でしょ) template static matrix map(const size_t n, const size_t m, LAMBDA f) { matrix r(n, m); for (size_t i = 0; i < n; i++) { for (size_t j = 0; j < m; j++) { r.value[i][j] = f(i, j); } } return r; } static matrix eye(const size_t n) { matrix r(n); for (size_t i = 0; i < n; i++) r.value[i][i] = 1; return r; } matrix operator+ (const matrix &a) { if (this->rows() != a.rows() || this->cols() != a.cols()) abort(); const size_t n = this->rows(); const size_t m = this->cols(); return matrix::map(n, m, [&](size_t i, size_t j) { // return this->value[i][j] + a.value[i][j]; return (this->value[i][j] + a.value[i][j]) % pdiv; }); } matrix operator- (const matrix &a) { if (this->rows() != a.rows() || this->cols() != a.cols()) abort(); const size_t n = this->rows(); const size_t m = this->cols(); return matrix::map(n, m, [&](size_t i, size_t j) { // return this->value[i][j] - a.value[i][j]; return (this->value[i][j] + pdiv - a.value[i][j]) % pdiv; }); } matrix operator* (const matrix &a) { if (this->cols() != a.rows()) abort(); const size_t n = this->rows(); const size_t m = this->cols(); const size_t q = a.cols(); return matrix::map(n, q, [&](size_t i, size_t j) { T term = 0; for (size_t k = 0; k < m; k++) // term += this->value[i][k] * a.value[k][j]; (term += this->value[i][k] * a.value[k][j]) %= pdiv; return term; }); } matrix& operator+= (const matrix &a) { matrix r = *this + a; this->value.swap(r.value); return *this; } matrix& operator-= (const matrix &a) { matrix r = *this - a; this->value.swap(r.value); return *this; } matrix& operator*= (const matrix &a) { matrix r = *this * a; this->value.swap(r.value); return *this; } matrix transpose() { const size_t n = this->rows(); const size_t m = this->cols(); return matrix::map(m, n, [&](size_t i, size_t j) { return this->value[j][i]; }); } matrix pow(long long int n) { if (n == 0) { return matrix::eye(n); } else if (n == 1) { return *this; } else { matrix temp = this->pow(n / 2); return n % 2 == 0 ? temp * temp : temp * temp * *this; } } }; template void DUMPMTR(const matrix &m) { size_t r = m.rows(), c = m.cols(); for (size_t i = 0; i < r; i++) { cerr << " ["[!i] << "["; for (size_t j = 0; j < c; j++) { cerr << setw(3) << m.get(i, j) << (j == c-1 ? "]" : ", "); } cerr << "]" << "\n]"[i == r-1]; } cerr << "\n"; } // 処理内容 int main() { ll a, b, n; cin >> a >> b >> n; matrix x0 = {{1}, {0}}; matrix shazo = { {a, b}, {1, 0} }; cout << (shazo.pow(n) * x0).get(1) << endl; }