/* #region Head */ // #include #include #include #include #include // assert.h #include // math.h #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i)) #define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i)) #define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i)) #define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d)) #define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d)) #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define CEIL(a, b) (((a) + (b)-1) / (b)) #define endl '\n' constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr int IINF = 1'000'000'007LL; // constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 constexpr ll MOD = 10; // constexpr ll MOD = 998244353; constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, const vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, const vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, array &arr) { // array 入力 REP(i, 0, SIZE(arr)) is >> arr[i]; return is; } template ostream &operator<<(ostream &os, const array &arr) { // array 出力 (for dump) os << "{"; REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, const pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, const T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, const map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, const um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, const set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } void pprint() { cout << endl; } template void pprint(Head &&head, Tail &&...tail) { cout << head; if (sizeof...(Tail) > 0) cout << ' '; pprint(move(tail)...); } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&...tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #ifndef ONLINE_JUDGE #define DEBUG_ #endif #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif #define VAR(type, ...) \ type __VA_ARGS__; \ cin >> __VA_ARGS__; template istream &operator,(istream &is, T &rhs) { return is >> rhs; } template ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; } struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = false; AtCoderInitialize() { ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) cout << unitbuf; } } ATCODER_INITIALIZE; void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { cout << (p ? "YES" : "NO") << endl; } /* #endregion */ // #include // using namespace atcoder; /* #region Mat */ template constexpr bool false_v = false; // 行列,==, !=, [] あたりは array と一緒 template class Mat : public array, H> { public: Mat() : array, H>() { fill(0); } Mat(const Num value) : array, H>() { fill(value); } Mat(std::initializer_list> init) : array, H>() { int i = 0; for (auto iter = init.begin(); iter != init.end(); ++iter) (*this)[i++] = array(*iter); } // 行列に別の行列を足す Mat &operator+=(const Mat &another) { REP(i, 0, H) REP(j, 0, W)(*this)[i][j] += another[i][j]; return *this; } // 行列から別の行列を引く Mat &operator-=(const Mat &another) { REP(i, 0, H) REP(j, 0, W)(*this)[i][j] -= another[i][j]; return *this; } // 行列に別の行列を右から掛ける // template Mat &operator*=(const Mat &another) { // Mat ret = {}; // REP(i, 0, H) REP(j, 0, AW) REP(k, 0, W) ret[i][j] += (*this)[i][k] * another[k][j]; // *this = ret; // return *this; // } // this を更新する場合,行列サイズが変わらない乗算のみ許容する(型が変わってしまうため) Mat &operator*=(const Mat &another) { Mat ret = (*this) * another; *this = ret; return *this; } // 行列に別の行列を足す Mat operator+(const Mat &another) const { Mat ret(*this); return ret += another; } // 行列から別の行列を引く Mat operator-(const Mat &another) const { Mat ret(*this); return ret -= another; } // 行列に別の行列を右から掛ける template Mat operator*(const Mat &another) const { // Mat ret(*this); // return ret *= another; Mat ret = {}; REP(i, 0, H) REP(j, 0, AW) REP(k, 0, W) ret[i][j] += (*this)[i][k] * another[k][j]; return ret; } // 行列の n 乗を計算する Mat pow(ll n) const { assert(H == W); Mat ret = {}; Mat a(*this); REP(i, 0, H) ret[i][i] = 1; while (n) { if (n & 1) ret = a * ret; a = a * a, n >>= 1; } return ret; } // 列和が 1 になるよう正規化する Mat norm() const { array s = {}; Mat a(*this); REP(i, 0, H) REP(j, 0, W) s[j] += a[i][j]; REP(i, 0, H) REP(j, 0, W) a[i][j] /= s[j]; return a; } // 行列の n 乗を計算する(列和が常に 1 になるよう正規化する) Mat pow_norm(ll n) const { assert(H == W); Mat ret = {}; Mat a(*this); REP(i, 0, H) ret[i][i] = 1; while (n) { if (n & 1) ret = (a * ret).norm(); a = (a * a).norm(), n >>= 1; } return ret; } template Mat assign(T... nums) { vc num_list = vc{nums...}; assert(SIZE(num_list) == H * W); REP(i, 0, H) REP(j, 0, W)(*this)[i][j] = num_list[W * i + j]; return *this; } void fill(Num num) { REP(i, 0, H) REP(j, 0, W)(*this)[i][j] = num; } void print() { REP(i, 0, H) REP(j, 0, W) cout << (*this)[i][j] << (j == W - 1 ? '\n' : ' '); } void dump_col(ll j) { REP(i, 0, H) cout << (*this)[i][j] << (i == H - 1 ? '\n' : ' '); } }; /* #endregion */ /* #region mint */ // 自動で MOD を取る整数 struct mint { ll x; mint(ll x = 0) : x((x % MOD + MOD) % MOD) {} mint &operator+=(const mint a) { if ((x += a.x) >= MOD) x -= MOD; return *this; } mint &operator-=(const mint a) { if ((x += MOD - a.x) >= MOD) x -= MOD; return *this; } mint &operator*=(const mint a) { (x *= a.x) %= MOD; return *this; } mint operator+(const mint a) const { mint res(*this); return res += a; } mint operator-(const mint a) const { mint res(*this); return res -= a; } mint operator*(const mint a) const { mint res(*this); return res *= a; } // O(log(t)) mint pow_rec(ll t) const { if (!t) return 1; mint a = pow(t >> 1); // ⌊t/2⌋ 乗 a *= a; // ⌊t/2⌋*2 乗 if (t & 1) // ⌊t/2⌋*2 == t-1 のとき a *= *this; // ⌊t/2⌋*2+1 乗 => t 乗 return a; } mint pow(ll t) const { mint a(*this); mint res = 1; while (t) { if (t & 1) res *= a; t >>= 1, a *= a; } return res; } // for prime mod mint inv_prime() const { return pow(MOD - 2); // オイラーの定理から, x^(-1) ≡ x^(p-2) } mint inv() const { ll a = this->x, b = MOD, u = 1, v = 0, t; mint res; while (b) { t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if (u < 0) u += MOD; res = u; return res; } mint &operator/=(const mint a) { return (*this) *= a.inv(); } mint operator/(const mint a) const { mint res(*this); return res /= a; } bool operator==(const mint a) const { return this->x == a.x; } bool operator==(const ll a) const { return this->x == a; } bool operator!=(const mint a) const { return this->x != a.x; } bool operator!=(const ll a) const { return this->x != a; } // mint 入力 friend istream &operator>>(istream &is, mint &x) { is >> x.x; return is; } // mint 出力 friend ostream &operator<<(ostream &os, const mint x) { os << x.x; return os; } }; /* #endregion */ // Problem void solve() { VAR(ll, p, q, r, k); // using mat = Mat; mat M{{1, 1, 1}, {1, 0, 0}, {0, 1, 0}}; M = M.pow(k - 3); Mat init{{r}, {q}, {p}}; Mat ans = M * init; pprint(ans[0][0]); } // entry point int main() { solve(); return 0; }