#define LOCAL #include using namespace std; #pragma region Macros typedef long long ll; typedef __int128_t i128; typedef unsigned int uint; typedef unsigned long long ull; #define ALL(x) (x).begin(), (x).end() template istream& operator>>(istream& is, vector& v) { for (T& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, const vector& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } template ostream& operator<<(ostream& os, const pair& p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream& operator<<(ostream& os, const map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const multiset& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const deque& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } template void print_tuple(ostream&, const T&) {} template void print_tuple(ostream& os, const T& t) { if (i) os << ','; os << get(t); print_tuple(os, t); } template ostream& operator<<(ostream& os, const tuple& t) { os << '{'; print_tuple<0, tuple, Args...>(os, t); return os << '}'; } void debug_out() { cerr << '\n'; } template void debug_out(Head&& head, Tail&&... tail) { cerr << head; if (sizeof...(Tail) > 0) cerr << ", "; debug_out(move(tail)...); } #ifdef LOCAL #define debug(...) \ cerr << " "; \ cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \ cerr << " "; \ debug_out(__VA_ARGS__) #else #define debug(...) 42 #endif template T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; } template T lcm(T x, T y) { return x / gcd(x, y) * y; } 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 botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); } int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); } int popcount(signed t) { return __builtin_popcount(t); } int popcount(long long t) { return __builtin_popcountll(t); } bool ispow2(int i) { return i && (i & -i) == i; } template T ceil(T x, T y) { assert(y >= 1); return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, T y) { assert(y >= 1); return (x > 0 ? x / y : (x - y + 1) / y); } template inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; } #pragma endregion /** * @brief 実行時 modint * @docs docs/modulo/modint.md */ class dynamic_modint { using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; static u32& mod() { static u32 mod_ = 0; return mod_; } public: u32 v; static void set_mod(const u32 x) { assert(x < (u32(1) << 31)); mod() = x; } static u32 get_mod() { return mod(); } dynamic_modint(const i64 x = 0) : v(x < 0 ? get_mod() - 1 - (-(x + 1) % get_mod()) : x % get_mod()) {} u32& value() noexcept { return v; } const u32& value() const noexcept { return v; } dynamic_modint operator+(const dynamic_modint& rhs) const { return dynamic_modint(*this) += rhs; } dynamic_modint operator-(const dynamic_modint& rhs) const { return dynamic_modint(*this) -= rhs; } dynamic_modint operator*(const dynamic_modint& rhs) const { return dynamic_modint(*this) *= rhs; } dynamic_modint operator/(const dynamic_modint& rhs) const { return dynamic_modint(*this) /= rhs; } dynamic_modint& operator+=(const dynamic_modint& rhs) { v += rhs.v; if (v >= get_mod()) v -= get_mod(); return *this; } dynamic_modint& operator-=(const dynamic_modint& rhs) { if (v < rhs.v) v += get_mod(); v -= rhs.v; return *this; } dynamic_modint& operator*=(const dynamic_modint& rhs) { v = (u64)v * rhs.v % get_mod(); return *this; } dynamic_modint& operator/=(const dynamic_modint& rhs) { return *this *= rhs.pow(get_mod() - 2); } dynamic_modint pow(u64 exp) const { dynamic_modint self(*this), res(1); while (exp > 0) { if (exp & 1) res *= self; self *= self; exp >>= 1; } return res; } dynamic_modint& operator++() { if (++v == get_mod()) v = 0; return *this; } dynamic_modint& operator--() { if (v == 0) v = get_mod(); return --v, *this; } dynamic_modint operator++(int) { dynamic_modint t = *this; return ++*this, t; } dynamic_modint operator--(int) { dynamic_modint t = *this; return --*this, t; } dynamic_modint operator-() { return dynamic_modint(get_mod() - v); } template friend dynamic_modint operator+(T x, dynamic_modint y) { return dynamic_modint(x) + y; } template friend dynamic_modint operator-(T x, dynamic_modint y) { return dynamic_modint(x) - y; } template friend dynamic_modint operator*(T x, dynamic_modint y) { return dynamic_modint(x) * y; } template friend dynamic_modint operator/(T x, dynamic_modint y) { return dynamic_modint(x) / y; } bool operator==(const dynamic_modint& rhs) { return v == rhs.v; } bool operator!=(const dynamic_modint& rhs) { return v != rhs.v; } bool operator!() { return !v; } friend istream& operator>>(istream& s, dynamic_modint& rhs) { i64 v; rhs = dynamic_modint{(s >> v, v)}; return s; } friend ostream& operator<<(ostream& s, const dynamic_modint& rhs) { return s << rhs.v; } }; /** * @brief combination * @docs docs/combinatorics/combination.md */ template struct Combination { vector _fac, _inv, _finv; Combination(int n) : _fac(n + 1), _inv(n + 1), _finv(n + 1) { _fac[0] = _finv[n] = _inv[0] = 1; for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i; _finv[n] /= _fac[n]; for (int i = n - 1; i >= 0; i--) _finv[i] = _finv[i + 1] * (i + 1); for (int i = 1; i <= n; i++) _inv[i] = _finv[i] * _fac[i - 1]; } M fac(int k) const { return _fac[k]; } M finv(int k) const { return _finv[k]; } M inv(int k) const { return _inv[k]; } M P(int n, int r) const { if (n < 0 || r < 0 || n < r) return 0; return _fac[n] * _finv[n - r]; } M C(int n, int r) const { if (n < 0 || r < 0 || n < r) return 0; return _fac[n] * _finv[r] * _finv[n - r]; } }; const int INF = 1e9; const long long IINF = 1e18; const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; const char dir[4] = {'D', 'R', 'U', 'L'}; const long long MOD = 1000000007; // const long long MOD = 998244353; using mint = dynamic_modint; int main() { cin.tie(0); ios::sync_with_stdio(false); int N, mod; cin >> N >> mod; mint::set_mod(mod); Combination COM(N + 1); vector tree(N + 1); // i 頂点のラベル付き木の数 tree[1] = 1; for (int i = 2; i <= N; i++) tree[i] = mint(i).pow(i - 2); vector> dp(N + 1, vector(N + 1, 0)); dp[0][0] = 1; for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { mint val = dp[i][j]; if (val == 0) continue; for (int k = 1; j + k <= N; k++) { dp[i + 1][j + k] += val * COM.C(N - j - 1, k - 1) * tree[k]; } } } for (int i = 0; i < N; i++) cout << dp[N - i][N] << '\n'; return 0; }