#pragma region competitive_programming #ifdef __LOCAL #define _GLIBCXX_DEBUG #endif #pragma GCC optimize("Ofast") #include //#include //#include "Rollback_dsu.hpp" //#include "Partial_Persistent_DSU.hpp" #include #include #include #include #include #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } struct barrett { unsigned int _m; unsigned long long im; explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} unsigned int umod() const { return _m; } unsigned int mul(unsigned int a, unsigned int b) const { unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template constexpr bool is_prime = is_prime_constexpr(n); constexpr std::pair inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if (m0 < 0) m0 += b / s; return {s, m0}; } constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template constexpr int primitive_root = primitive_root_constexpr(m); unsigned long long floor_sum_unsigned(unsigned long long n, unsigned long long m, unsigned long long a, unsigned long long b) { unsigned long long ans = 0; while (true) { if (a >= m) { ans += n * (n - 1) / 2 * (a / m); a %= m; } if (b >= m) { ans += n * (b / m); b %= m; } unsigned long long y_max = a * n + b; if (y_max < m) break; n = (unsigned long long)(y_max / m); b = (unsigned long long)(y_max % m); std::swap(m, a); } return ans; } } // namespace internal } // namespace atcoder namespace atcoder { long long pow_mod(long long x, long long n, int m) { assert(0 <= n && 1 <= m); if (m == 1) return 0; internal::barrett bt((unsigned int)(m)); unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m)); while (n) { if (n & 1) r = bt.mul(r, y); y = bt.mul(y, y); n >>= 1; } return r; } long long inv_mod(long long x, long long m) { assert(1 <= m); auto z = internal::inv_gcd(x, m); assert(z.first == 1); return z.second; } std::pair crt(const std::vector& r, const std::vector& m) { assert(r.size() == m.size()); int n = int(r.size()); long long r0 = 0, m0 = 1; for (int i = 0; i < n; i++) { assert(1 <= m[i]); long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i]; if (m0 < m1) { std::swap(r0, r1); std::swap(m0, m1); } if (m0 % m1 == 0) { if (r0 % m1 != r1) return {0, 0}; continue; } long long g, im; std::tie(g, im) = internal::inv_gcd(m0, m1); long long u1 = (m1 / g); if ((r1 - r0) % g) return {0, 0}; long long x = (r1 - r0) / g % u1 * im % u1; r0 += x * m0; m0 *= u1; // -> lcm(m0, m1) if (r0 < 0) r0 += m0; } return {r0, m0}; } long long floor_sum(long long n, long long m, long long a, long long b) { assert(0 <= n && n < (1LL << 32)); assert(1 <= m && m < (1LL << 32)); unsigned long long ans = 0; if (a < 0) { unsigned long long a2 = internal::safe_mod(a, m); ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m); a = a2; } if (b < 0) { unsigned long long b2 = internal::safe_mod(b, m); ans -= 1ULL * n * ((b2 - b) / m); b = b2; } return ans + internal::floor_sum_unsigned(n, m, a, b); } } // namespace atcoder //#include "modint_plus.hpp" //typedef atcoder::modint1000000007 mint; //typedef atcoder::modint998244353 mint; //#include "Matrix.hpp" //#include //#include "Formal_Power_Series.hpp" //#include "Bit_Convolution.hpp" //#include //#include //#include "Primal_Dual.hpp" //#include "maxflow_mincap.hpp" //#include //#include //#include //#include "2D_Segment_Tree.hpp" //#include "DisjointSparseTable.hpp" //#include "SWAG.hpp" //#include "Mo_algorithm.hpp" //#include "Heavy_Light_Decomposition.hpp" //#include "Binary_Trie.hpp" //#include "LCT.hpp" //#include "Slope_Trick.hpp" //#include //#include namespace tomo0608 { typedef long long ll; typedef long double ld; template using V = std::vector; template using VV = V>; template using VVV = V>; typedef std::pair pii; typedef std::pair pll; templatevoid input(T&... a) { (std::cin >> ... >> a); }; #define INT(...) int __VA_ARGS__; IN(__VA_ARGS__) #define LL(...) long long __VA_ARGS__; IN(__VA_ARGS__) #define STR(...) string __VA_ARGS__; IN(__VA_ARGS__) #define DBL(...) double __VA_ARGS__; IN(__VA_ARGS__) #define VEC(type, name, size) std::vector name(size);IN(name) #define VECVEC(type, name, h, w) std::vector> name(h, std::vector(w));IN(name) template std::istream& operator>>(std::istream& is, std::pair& p) { is >> p.first >> p.second; return is; } template std::ostream& operator<<(std::ostream& os, const std::pair& p) { os << '(' << p.first << ", " << p.second << ')'; return os; } template std::istream& operator>>(std::istream& is, std::vector& v) { for (auto& e : v) is >> e; return is; } template std::ostream& operator<<(std::ostream& os, const std::vector& v) { for (auto& e : v) os << e << ' '; return os; } template std::ostream& operator << (std::ostream& os, std::set& set_var) { os << "{"; for (auto itr = set_var.begin(); itr != set_var.end(); itr++) { os << *itr;++itr;if (itr != set_var.end()) os << ", ";itr--; }os << "}";return os; } template std::ostream& operator<<(std::ostream& os, std::map& map_var) { os << "{";for (auto itr = map_var.begin(); itr != map_var.end(); itr++) { os << *itr;itr++;if (itr != map_var.end()) os << ", ";itr--; }os << "}";return os; } void IN() {} template void IN(Head& head, Tail &...tail) { std::cin >> head; IN(tail...); } void print() { std::cout << '\n'; } templatevoid print(const T& a, const Ts&... b) { std::cout << a; (std::cout << ... << (std::cout << ' ', b)); std::cout << '\n'; } void drop() { std::cout << '\n';exit(0); } templatevoid drop(const T& a, const Ts&... b) { std::cout << a; (std::cout << ... << (std::cout << ' ', b)); std::cout << '\n';exit(0); } #ifdef __LOCAL void debug_out() { std::cerr << std::endl; } template < class Head, class... Tail> void debug_out(Head H, Tail... T) { std::cerr << ' ' << H; debug_out(T...); } #define debug(...) std::cerr << 'L' << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__) #define dump(x) std::cerr << 'L' << __LINE__ << " " << #x << " = " << (x) << std::endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif #define rep1(a) for(long long i = 0; i < a; i++) #define rep2(i, a) for(long long i = 0; i < a; i++) #define rep3(i, a, b) for(long long i = a; i < b; i++) #define rep4(i, a, b, c) for(long long i = a; i < b; i += c) #define drep1(a) for(long long i = a-1; i >= 0; i--) #define drep2(i, a) for(long long i = a-1; i >= 0; i--) #define drep3(i, a, b) for(long long i = a-1; i >= b; i--) #define drep4(i, a, b, c) for(long long i = a-1; i >= b; i -= c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define drep(...) overload4(__VA_ARGS__, drep4, drep3, drep2, drep1)(__VA_ARGS__) #define endl '\n' } // namespace tomo0608 namespace tomo0608 { #define ALL(x) x.begin(),x.end() template T SUM(const S& v) { return accumulate(ALL(v), T(0)); } #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define SORT(v) sort(ALL(v)) #define REVERSE(v) reverse(ALL(v)) #define RSORT(v) sort(ALL(v)); reverse(ALL(v)) #define UNIQUE(x) SORT(x), x.erase(unique(ALL(x)), x.end()) #define lb(c, x) distance((c).begin(), lower_bound(ALL(c), (x))) #define ub(c, x) distance((c).begin(), upper_bound(ALL(c), (x))) template void zip(std::vector& x) { std::vector y = x;UNIQUE(y);for (int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); } } template using priority_queue_rev = std::priority_queue, std::greater>; template inline bool chmax(T& a, const U& b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, const U& b) { if (a > b) { a = b; return 1; } return 0; } template inline int count_between(std::vector& a, T l, T r) { return lower_bound(all(a), r) - lower_bound(all(a), l); } // [l, r) #define bittest(n, k) ((n >> k) & 1) int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); } int lowbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); } #define perm(v) for(bool permrepflag = true; (permrepflag ? exchange(permrepflag, false) : next_permutation(ALL(v)));) template T ceil(T x, S y) { assert(y); return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y)); } template T floor(T x, S y) { assert(y); return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1))); } } using namespace atcoder; using namespace std; using namespace tomo0608; int dx[8] = { 1, 0, -1, 0, 1, 1, -1, -1 }; int dy[8] = { 0, 1, 0, -1, 1, -1, -1, 1 }; // インタラクティブ問題のときは出力するたびにcout.flush();を忘れない!!!!! void solve(); int main() { std::cin.tie(0); std::ios_base::sync_with_stdio(false); std::cout << std::setprecision(20); int codeforces = 1; //cin >> codeforces; while (codeforces--) { solve(); } return 0; } #pragma endregion void solve() { LL(n, p); // n!がpでなんかいわれるか ll e = 0; while (n > 0) { e += (n / p); n /= p; } print(pow_mod(p, e, 998244353)); }