//#define _GLIBCXX_DEBUG #include using namespace std; #define endl '\n' #define lfs cout<= (ll)(n); i--) using ll = long long; using ld = long double; const ll MOD1 = 1e9+7; const ll MOD9 = 998244353; const ll INF = 1e18; using P = pair; template using PQ = priority_queue; template using QP = priority_queue,greater>; templatebool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;} templatebool chmax(T1 &a,T2 b){if(avoid ans(bool x,T1 y,T2 z){if(x)cout<void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);}; templatevoid debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;ivoid debug(const T &v,ll n,string sv=" "){if(n!=0)cout<void debug(const vector&v){debug(v,v.size());} templatevoid debug(const vector>&v){for(auto &vv:v)debug(vv,vv.size());} templatevoid debug(stack st){while(!st.empty()){cout<void debug(queue st){while(!st.empty()){cout<void debug(deque st){while(!st.empty()){cout<void debug(PQ st){while(!st.empty()){cout<void debug(QP st){while(!st.empty()){cout<void debug(const set&v){for(auto z:v)cout<void debug(const multiset&v){for(auto z:v)cout<void debug(const array &a){for(auto z:a)cout<void debug(const map&v){for(auto z:v)cout<<"["<vector>vec(ll x, ll y, T w){vector>v(x,vector(y,w));return v;} ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;} vectordx={1,-1,0,0,1,1,-1,-1};vectordy={0,0,1,-1,1,-1,1,-1}; templatevector make_v(size_t a,T b){return vector(a,b);} templateauto make_v(size_t a,Ts... ts){return vector(a,make_v(ts...));} templateostream &operator<<(ostream &os, const pair&p){return os << p.first << " " << p.second;} templateostream &operator<<(ostream &os, const vector &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;} templatevoid rearrange(vector&ord, vector&v){ auto tmp = v; for(int i=0;ivoid rearrange(vector&ord,Head&& head, Tail&&... tail){ rearrange(ord, head); rearrange(ord, tail...); } template vector ascend(const vector&v){ vectorord(v.size());iota(ord.begin(),ord.end(),0); sort(ord.begin(),ord.end(),[&](int i,int j){return v[i] vector descend(const vector&v){ vectorord(v.size());iota(ord.begin(),ord.end(),0); sort(ord.begin(),ord.end(),[&](int i,int j){return v[i]>v[j];}); return ord; } ll FLOOR(ll n,ll div){return n>=0?n/div:(n-div+1)/div;} ll CEIL(ll n,ll div){return n>=0?(n+div-1)/div:n/div;} ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;} templateT min(const vector&v){return *min_element(v.begin(),v.end());} templateT max(const vector&v){return *max_element(v.begin(),v.end());} templateT acc(const vector&v){return accumulate(v.begin(),v.end(),T(0));}; templateT reverse(const T &v){return T(v.rbegin(),v.rend());}; //mt19937 mt(chrono::steady_clock::now().time_since_epoch().count()); int popcount(ll x){return __builtin_popcountll(x);}; int poplow(ll x){return __builtin_ctzll(x);}; int pophigh(ll x){return 63 - __builtin_clzll(x);}; templateT poll(queue &q){auto ret=q.front();q.pop();return ret;}; templateT poll(priority_queue &q){auto ret=q.top();q.pop();return ret;}; templateT poll(QP &q){auto ret=q.top();q.pop();return ret;}; templateT poll(stack &s){auto ret=s.top();s.pop();return ret;}; template< typename T = int > struct edge { int to; T cost; int id; edge():id(-1){}; edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){} operator int() const { return to; } }; template using Graph = vector>>; template Graphrevgraph(const Graph &g){ Graphret(g.size()); for(int i=0;i Graph readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){ Graph ret(n); for(int es = 0; es < m; es++){ int u,v; T w=1; cin>>u>>v;u-=indexed,v-=indexed; if(weighted)cin>>w; ret[u].emplace_back(v,w,es); if(!directed)ret[v].emplace_back(u,w,es); } return ret; } template Graph readParent(int n,int indexed=1,bool directed=true){ Graphret(n); for(int i=1;i>p; p-=indexed; ret[p].emplace_back(i); if(!directed)ret[i].emplace_back(p); } return ret; } namespace atcoder { namespace internal { #ifndef _MSC_VER template using is_signed_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using is_unsigned_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using make_unsigned_int128 = typename std::conditional::value, __uint128_t, unsigned __int128>; template using is_integral = typename std::conditional::value || is_signed_int128::value || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using is_signed_int = typename std::conditional<(is_integral::value && std::is_signed::value) || is_signed_int128::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional<(is_integral::value && std::is_unsigned::value) || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional< is_signed_int128::value, make_unsigned_int128, typename std::conditional::value, std::make_unsigned, std::common_type>::type>::type; #else template using is_integral = typename std::is_integral; template using is_signed_int = typename std::conditional::value && std::is_signed::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional::value && std::is_unsigned::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional::value, std::make_unsigned, std::common_type>::type; #endif template using is_signed_int_t = std::enable_if_t::value>; template using is_unsigned_int_t = std::enable_if_t::value>; template using to_unsigned_t = typename to_unsigned::type; } // namespace internal } // namespace atcoder namespace atcoder { namespace internal { // @param m `1 <= m` // @return x mod m constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } // Fast moduler by barrett reduction // Reference: https://en.wikipedia.org/wiki/Barrett_reduction // NOTE: reconsider after Ice Lake struct barrett { unsigned int _m; unsigned long long im; // @param m `1 <= m` barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} // @return m unsigned int umod() const { return _m; } // @param a `0 <= a < m` // @param b `0 <= b < m` // @return `a * b % m` unsigned int mul(unsigned int a, unsigned int b) const { // [1] m = 1 // a = b = im = 0, so okay // [2] m >= 2 // im = ceil(2^64 / m) // -> im * m = 2^64 + r (0 <= r < m) // let z = a*b = c*m + d (0 <= c, d < m) // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2 // ((ab * im) >> 64) == c or c + 1 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; } }; // @param n `0 <= n` // @param m `1 <= m` // @return `(x ** n) % m` 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; } // Reference: // M. Forisek and J. Jancina, // Fast Primality Testing for Integers That Fit into a Machine Word // @param n `0 <= n` 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; for (long long a : {2, 7, 61}) { 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); // @param b `1 <= b` // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g constexpr std::pair inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b 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 // [3]: // (s - t * u) * |m1| + t * |m0 - m1 * u| // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u) // = s * |m1| + t * |m0| <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if (m0 < 0) m0 += b / s; return {s, m0}; } // Compile time primitive root // @param m must be prime // @return primitive root (and minimum in now) 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); } // namespace internal } // namespace atcoder namespace atcoder { namespace internal { struct modint_base {}; struct static_modint_base : modint_base {}; template using is_modint = std::is_base_of; template using is_modint_t = std::enable_if_t::value>; } // namespace internal template * = nullptr> struct static_modint : internal::static_modint_base { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } static_modint() : _v(0) {} template * = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template * = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); } static_modint(bool v) { _v = ((unsigned int)(v) % umod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } mint& operator*=(const mint& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = internal::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = internal::is_prime; }; template struct dynamic_modint : internal::modint_base { using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = internal::barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template * = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template * = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); } dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = internal::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static internal::barrett bt; static unsigned int umod() { return bt.umod(); } }; template internal::barrett dynamic_modint::bt = 998244353; using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; namespace internal { template using is_static_modint = std::is_base_of; template using is_static_modint_t = std::enable_if_t::value>; template struct is_dynamic_modint : public std::false_type {}; template struct is_dynamic_modint> : public std::true_type {}; template using is_dynamic_modint_t = std::enable_if_t::value>; } // namespace internal } // namespace atcoder template< typename T > struct Combination { vector< T > _fact, _rfact, _inv; Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) { _fact[0] = _rfact[sz] = _inv[0] = 1; for(ll i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i; _rfact[sz] /= _fact[sz]; for(ll i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1); for(ll i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1]; } inline T fact(ll k) const { return _fact[k]; } inline T rfact(ll k) const { return _rfact[k]; } inline T inv(ll k) const { return _inv[k]; } T P(ll n, ll r) const { if(r < 0 || n < r) return 0; return fact(n) * rfact(n - r); } T C(ll p, ll q) const { if(q < 0 || p < q) return 0; return fact(p) * rfact(q) * rfact(p - q); } T RC(ll p, ll q) const { if(q < 0 || p < q) return 0; return rfact(p) * fact(q) * fact(p - q); } T H(ll n, ll r) const { if(n < 0 || r < 0) return (0); return r == 0 ? 1 : C(n + r - 1, r); } }; int main(){ cin.tie(nullptr); ios_base::sync_with_stdio(false); ll res=0,buf=0; bool judge = true; using atcoder::modint; ll n,mod;cin>>n>>mod; modint::set_mod(mod); Combinationcomb(10000); auto dp=vec(n+1,n,modint(0)); dp[0][0]=1; vectork(n+1); rep(i,1,n+1){ if(i==1)k[i]=1; else k[i]=modint(i).pow(i-2); } rep(i,0,n){ rep(j,0,n){ rep(o,1,n+1){ if(i+o>n||j+o-1>=n)continue; dp[i+o][j+o-1]+=dp[i][j]*comb.C(n-i-1,o-1)*k[o]; } } } rep(i,0,n)cout<