//#define NDEBUG #pragma warning(disable : 4146) #include namespace n91 { using i32 = std::int32_t; using i64 = std::int64_t; using u32 = std::uint32_t; using u64 = std::uint64_t; using isize = std::ptrdiff_t; using usize = std::size_t; using f64 = double; struct rep { struct itr { usize i; constexpr itr(const usize i) noexcept : i(i) {} void operator++() noexcept { ++i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; const itr f, l; constexpr rep(const usize f, const usize l) noexcept : f(std::min(f, l)), l(l) {} constexpr auto begin() const noexcept { return f; } constexpr auto end() const noexcept { return l; } }; struct revrep { struct itr { usize i; constexpr itr(const usize i) noexcept : i(i) {} void operator++() noexcept { --i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; const itr f, l; constexpr revrep(const usize f, const usize l) noexcept : f(l - 1), l(std::min(f, l) - 1) {} constexpr auto begin() const noexcept { return f; } constexpr auto end() const noexcept { return l; } }; template auto md_vec(const usize n, const T& value) { return std::vector(n, value); } template auto md_vec(const usize n, Args... args) { return std::vector(n, md_vec(args...)); } template constexpr T difference(const T& a, const T& b) noexcept { return a < b ? b - a : a - b; } template void chmin(T& a, const T& b) noexcept { if (b < a) a = b; } template void chmax(T& a, const T& b) noexcept { if (a < b) a = b; } template class rec_lambda { F f; public: rec_lambda(F&& f_) : f(std::forward(f_)) {} template auto operator()(Args &&... args) const { return f(*this, std::forward(args)...); } }; template T scan() { T ret; std::cin >> ret; return ret; } constexpr char eoln = '\n'; i64 floor_div(const i64 n, const i64 d) { assert(d != 0); return n / d - static_cast((n ^ d) < 0 && n % d != 0); } i64 ceil_div(const i64 n, const i64 d) { assert(d != 0); return n / d + static_cast((n ^ d) >= 0 && n % d != 0); } #ifdef N91_LOCAL #define OJ_LOCAL(a, b) b #else #define OJ_LOCAL(a, b) a #endif } // namespace n91 #include #include #include namespace noshi91 { template class mint_utility { static inline std::vector fact_ = { T::raw(1) }; static inline std::vector inv_fact_ = { T::raw(1) }; static void extend(const int n) { const int s = fact_.size(); if (n >= s) { int t = s; while (n >= t) t = std::min(t * 2, T::mod()); fact_.resize(t); inv_fact_.resize(t); for (int i = s; i < t; i++) { fact_[i] = fact_[i - 1] * T::raw(i); } inv_fact_.back() = T::raw(1) / fact_.back(); for (int i = t - 1; i > s; i--) { inv_fact_[i - 1] = inv_fact_[i] * T::raw(i); } } } public: mint_utility() = delete; static T fact(const int n) { assert(0 <= n && n < T::mod()); extend(n); return fact_[n]; } static T inv_fact(const int n) { assert(0 <= n && n < T::mod()); extend(n); return inv_fact_[n]; } static T binom(const int n, const int r) { assert(0 <= n && n < T::mod()); if (r < 0 || n < r) { return T::raw(0); } else { extend(n); return fact_[n] * inv_fact_[r] * inv_fact_[n - r]; } } static T binom2(const int a, const int b) { assert(0 <= a && 0 <= b && a + b < T::mod()); extend(a + b); return fact_[a + b] * inv_fact_[a] * inv_fact_[b]; } static T homo(const int n, const int r) { assert(1 <= n); if (r < 0) return T::raw(0); assert(n + r - 1 < T::mod()); extend(n + r - 1); return fact_[n + r - 1] * inv_fact_[n - 1] * inv_fact_[r]; } static T perm(const int n, const int r) { assert(0 <= r && n < T::mod()); if (n < r) { return T::raw(0); } else { extend(n); return fact_[n] * inv_fact_[n - r]; } } }; } // namespace noshi91 #include using mint = atcoder::modint998244353; #include #include namespace n91 { void main_() { using mp = atcoder::modint; using util = noshi91::mint_utility; const u64 n = scan(); const u64 p = scan(); mp::set_mod(p); std::vector exp(p - 1), log(p, -1); { const u64 g = atcoder::internal::primitive_root_constexpr(p); u64 t = 1; for (const usize i : rep(0, p - 1)) { exp[i] = t; log[t] = i; t = (t * g) % p; } } auto res = rec_lambda([&](const auto& f, const u64 n) -> std::vector { if (n == 0) { return std::vector(p - 1, 0); } auto ret = f(n / p); std::vector all(p - 1, 0); for (const usize i : rep(0, p)) { const usize c = util::binom(n % p, i).val(); if (c != 0) all[log[c]] += 1; } ret = atcoder::convolution(ret, all); for (const usize i : rep(p - 1, ret.size())) ret[i % (p - 1)] += ret[i]; ret.resize(p - 1); for (const usize i : rep(0, n% p)) { const usize c = util::binom(n % p, i).val(); if (c != 0) ret[log[c]] += 1; } return ret; })(n); mint ans = 1; for (const usize i : rep(0, p - 1)) { ans += mint(exp[i]) * res[i]; } std::cout << ans.val() << eoln; } } // namespace n91 int main() { //* std::ios::sync_with_stdio(false); std::cin.tie(nullptr); //*/ std::cout << std::fixed << std::setprecision(20); n91::main_(); return 0; }