#include using namespace std; 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 tie(a, b) < tie(other.a, 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; } }; template int solve(uint64_t M, uint64_t D, uint64_t N) { using mint = Modint; map press; for(int i = 0; i < 1000; i++) press.try_emplace(i, press.size()); vector table(60, vector(press.size())); for(auto& [m, idx] : press) { table[0][idx] = press[(m + mint{D}).pow(m)]; } for(int l = 0; l + 1 < 60; l++) for(int i = 0; i < press.size(); i++) table[l + 1][i] = table[l][table[l][i]]; int ans = press[mint{M}]; for(int l = 0; l < 60; l++) if(N & 1ULL << l) ans = table[l][ans]; for(auto& [m, idx] : press) if(ans == idx) return m.a % B; abort(); } int main() { uint64_t M, D, N, B; cin >> M >> D >> N >> B; const int ans = [&]{ switch (B) { case 2: return solve<2>(M, D, N); case 3: return solve<3>(M, D, N); case 4: return solve<4>(M, D, N); case 5: return solve<5>(M, D, N); case 6: return solve<6>(M, D, N); case 7: return solve<7>(M, D, N); case 8: return solve<8>(M, D, N); case 9: return solve<9>(M, D, N); case 10: return solve<10>(M, D, N); default: return solve<11>(M, D, N); } }(); cout << hex << uppercase << ans << endl; }