#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif // https://trap.jp/post/1444/ constexpr uint32_t totient(uint32_t x){ uint32_t ans = x; for(uint32_t i = 2; i * i <= x; i++) if(x % i == 0){ ans /= i; ans *= i - 1; do x /= i; while(x % i == 0); } if(x != 1){ ans /= x; ans *= x - 1; } return ans; } template struct Modint{ static_assert(P < 0x80000000, "P must be smaller than 2^31"); uint32_t a; Modint b; private: static uint32_t mod(uint64_t x){ if(x < P * 2) return uint32_t(x); return uint32_t(x % P) + P; } static uint32_t mul(uint32_t a, uint32_t b){ return mod(uint64_t(a) * b); } static uint32_t pow(uint32_t a, uint32_t b){ uint32_t ans = 1; while(b){ if(b & 1) ans = mul(ans, a); a = mul(a, a); b >>= 1; } return ans; } public: Modint(uint64_t x): a(mod(x)), b(x){} Modint(uint32_t a, Modint b): a(a), b(b){} uint32_t val() const { if(a < P) return a; return a - P; } Modint& operator*=(const Modint& other){ a = mul(a, other.a); b *= other.b; return *this; } Modint operator*(const Modint& other) const { return Modint(*this) *= other; } Modint& operator+=(const Modint& other){ a += other.a; if(a >= P * 2) a -= P; if(a >= P * 2) a -= P; b += other.b; return *this; } Modint operator+(const Modint& other) const { return Modint(*this) += other; } Modint pow(const Modint& other) const { return {pow(a, other.b.a), b.pow(other.b)}; }; bool operator==(const Modint &other) const { return a == other.a and b == other.b; } }; template<> struct Modint<1>{ uint32_t a; Modint(uint64_t x): a(bool(x)){} uint32_t val() const { return 0; } Modint& operator*=(const Modint& other){ a &= other.a; return *this; } Modint operator*(const Modint& other) const { return Modint(*this) *= other; } Modint& operator+=(const Modint& other){ a |= other.a; return *this; } Modint operator+(const Modint& other) const { return Modint(*this) += other; } Modint pow(const Modint& other) const { return {a || !other.a}; } bool operator==(const Modint &other) const { return a == other.a; } }; string target_nums = "0123456789A"; template char solve(lint M, lint D, lint N) { vector> seq; seq.push_back(Modint(M)); for (lint t = 0; t < N; ++t) { auto nxt = (seq.back() + Modint(D)).pow(seq.back()); for (int s = 1000; s < t; ++s) { if (seq.at(s) == nxt) { int circ = t + 1 - s; const int rem = (N - t - 1) % circ; return target_nums.at(seq.at(s + rem).val()); } } seq.push_back(nxt); } return target_nums.at(seq.back().val()); } int main() { lint M, D, N; int B; cin >> M >> D >> N >> B; if (B == 2) cout << solve<2>(M, D, N) << endl; if (B == 3) cout << solve<3>(M, D, N) << endl; if (B == 4) cout << solve<4>(M, D, N) << endl; if (B == 5) cout << solve<5>(M, D, N) << endl; if (B == 6) cout << solve<6>(M, D, N) << endl; if (B == 7) cout << solve<7>(M, D, N) << endl; if (B == 8) cout << solve<8>(M, D, N) << endl; if (B == 9) cout << solve<9>(M, D, N) << endl; if (B == 10) cout << solve<10>(M, D, N) << endl; if (B == 11) cout << solve<11>(M, D, N) << endl; }