#include #define REP_(i, a_, b_, a, b, ...) \ for (int i = (a), END_##i = (b); i < END_##i; ++i) #define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__) #define ALL(x) std::begin(x), std::end(x) using i64 = long long; #include using Mint = atcoder::dynamic_modint<0>; std::ostream &operator<<(std::ostream &os, const Mint &m) { return os << m.val(); } template inline bool chmax(T &a, U b) { return a < b and ((a = std::move(b)), true); } template inline bool chmin(T &a, U b) { return a > b and ((a = std::move(b)), true); } template inline int ssize(const T &a) { return (int) std::size(a); } template std::istream &operator>>(std::istream &is, std::vector &a) { for (auto &x: a) is >> x; return is; } template std::ostream &operator<<(std::ostream &os, const std::pair &a) { return os << "(" << a.first << ", " << a.second << ")"; } template std::ostream &print_seq(const Container &a, std::string_view sep = " ", std::string_view ends = "\n", std::ostream &os = std::cout) { auto b = std::begin(a), e = std::end(a); for (auto it = std::begin(a); it != e; ++it) { if (it != b) os << sep; os << *it; } return os << ends; } template struct is_iterable : std::false_type {}; template struct is_iterable())), decltype(std::end(std::declval()))>> : std::true_type { }; template::value && !std::is_same::value && !std::is_same::value>> std::ostream &operator<<(std::ostream &os, const T &a) { return print_seq(a, ", ", "", (os << "{")) << "}"; } void print() { std::cout << "\n"; } template void print(const T &x) { std::cout << x << "\n"; } template void print(const Head &head, Tail... tail) { std::cout << head << " "; print(tail...); } struct Input { template operator T() const { T x; std::cin >> x; return x; } } in; #ifdef MY_DEBUG #include "debug_dump.hpp" #else #define DUMP(...) #endif using namespace std; // mod: prime template struct Factorials { // factorials and inverse factorials. std::vector fact, ifact; // n: max cached value. Factorials(int n) : fact(n + 1), ifact(n + 1) { assert(n >= 0); assert(n < T::mod()); fact[0] = 1; for (int i = 1; i <= n; ++i) { fact[i] = fact[i - 1] * i; } ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) { ifact[i - 1] = ifact[i] * i; } } // Combination (nCk) T C(int n, int k) const { if (k < 0 || k > n) return 0; return fact[n] * ifact[k] * ifact[n - k]; } }; int main() { ios_base::sync_with_stdio(false), cin.tie(nullptr); int n = in; int mod = in; Mint::set_mod(mod); Factorials fs(n); auto g = [&](int n) -> Mint { if (n <= 2) return 1; return Mint(n).pow(n - 2); }; vector memo(n + 1, vector(n + 1, optional())); auto f = [&](auto &f, int n, int m) -> Mint { if (m < 0) return 0; if (n <= 1) return (m == 0) ? 1 : 0; if (memo[n][m].has_value()) return memo[n][m].value(); Mint ret = 0; for (int i = 1; i <= n; ++i) { ret += fs.C(n - 1, i - 1) * g(i) * f(f, n - i, m - i + 1); } memo[n][m] = ret; return ret; }; REP(j, n) { print(f(f, n, j)); } }