/* #region Head */ // #include #include #include #include #include // assert.h #include // math.h #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define CEIL(a, b) (((a) + (b)-1) / (b)) #define endl '\n' constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr int IINF = 1'000'000'007LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 // constexpr ll MOD = 998244353; constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, const vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, const vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, array &arr) { // array 入力 REP(i, 0, SIZE(arr)) is >> arr[i]; return is; } template ostream &operator<<(ostream &os, const array &arr) { // array 出力 (for dump) os << "{"; REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, const pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, const T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, const map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, const um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, const set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } void pprint() { cout << endl; } template void pprint(Head &&head, Tail &&...tail) { cout << head; if (sizeof...(Tail) > 0) cout << ' '; pprint(move(tail)...); } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&...tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #ifndef ONLINE_JUDGE #define DEBUG_ #endif #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif #define VAR(type, ...) \ type __VA_ARGS__; \ cin >> __VA_ARGS__; template istream &operator,(istream &is, T &rhs) { return is >> rhs; } template ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; } struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = false; AtCoderInitialize() { ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) cout << unitbuf; } } ATCODER_INITIALIZE; void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { cout << (p ? "YES" : "NO") << endl; } /* #endregion */ // #include // using namespace atcoder; /* #region mint2 */ // 自動で mod を取る整数 (mod を動的に決める版) struct mint { ll mod; ll x; mint(ll mod, ll x) : mod(mod), x((x % mod + mod) % mod) {} // mint(const mint &another) : mod(another.mod), x(another.x) {} mint() : mod(0), x(0) {} mint &operator+=(const mint a) { assert(a.mod == mod); if ((x += a.x) >= mod) x -= mod; return *this; } mint &operator+=(const ll a) { if ((x += a % mod) >= mod) x -= mod; return *this; } mint &operator-=(const mint a) { assert(a.mod == mod); if ((x += mod - a.x) >= mod) x -= mod; return *this; } mint &operator-=(const ll a) { if ((x += mod - (a % mod)) >= mod) x -= mod; return *this; } mint &operator*=(const mint a) { assert(a.mod == mod); (x *= a.x) %= mod; return *this; } mint &operator*=(const ll a) { // (x *= a % mod) %= mod; *this *= mint(mod, a); return *this; } mint operator+(const mint a) const { mint res(*this); return res += a; } mint operator+(const ll a) const { mint res(*this); return res += a; } mint operator-(const mint a) const { mint res(*this); return res -= a; } mint operator-(const ll a) const { mint res(*this); return res -= a; } mint operator*(const mint a) const { mint res(*this); return res *= a; } mint operator*(const ll a) const { mint res(*this); return res *= a; } // O(log(t)) mint pow(ll t) const { if (!t) return mint(mod, 1); mint a = pow(t >> 1); // ⌊t/2⌋ 乗 a *= a; // ⌊t/2⌋*2 乗 if (t & 1) // ⌊t/2⌋*2 == t-1 のとき a *= *this; // ⌊t/2⌋*2+1 乗 => t 乗 return a; } // for prime mod mint inv_prime() const { return pow(mod - 2); // オイラーの定理から, x^(-1) ≡ x^(p-2) } mint inv() const { ll a = this->x, b = mod, u = 1, v = 0, t; // mint res; while (b) { t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if (u < 0) u += mod; mint res(mod, u); return res; } mint &operator/=(const mint a) { return (*this) *= a.inv(); } mint &operator/=(const ll a) { return (*this) *= mint(mod, a).inv(); } mint operator/(const mint a) const { mint res(*this); return res /= a; } mint operator/(const ll a) const { mint res(*this); return res /= a; } bool operator==(const mint a) const { return this->x == a.x; } bool operator==(const ll a) const { return this->x == a % mod; } // mint 入力 friend istream &operator>>(istream &is, mint &x) { is >> x.x; return is; } // mint 出力 friend ostream &operator<<(ostream &os, mint x) { os << x.x; return os; } }; /* #endregion */ // Problem void solve() { VAR(ll, n, m); // // 長さ 2N -> 0, 1 それぞれ N 個 // N=2 なら 0011, 0101 // valid な括弧列と同じ // 転倒数は必ず 0 以上 N-1 以下 // dp[i][j][k] := i 番目まで見て,1 を j 個使って,転倒数が k であるような場合の数 vc>> dp(2 * n, vc>(n + 1, vc(n * (n - 1) + 1, mint(m, 0)))); dp[0][0][0] += 1; // dump(dp[0]); REP(i, 1, 2 * n) { REPM(j, max(0LL, i - n), min(i, n)) REPM(k, 0, min(n * (n - 1), i * (i + 1))) { // 1 を使う分には転倒数は増えない if (j + 1 <= (i + 1) / 2) dp[i][j + 1][k] += dp[i - 1][j][k]; // 1 を j 個使用済み→ここで 0 を使うと,転倒数が +j される // 0 の個数 (i+1)-j は n を超えない if ((i + 1) - j <= n && k + j <= n * (n - 1)) { dp[i][j][k + j] += dp[i - 1][j][k]; } } // dump(dp[i]); } // dump(dp); REPM(k, 0, n * n) { if (k <= n * (n - 1)) pprint(dp[2 * n - 1][n][k]); else pprint(0); } } // entry point int main() { solve(); return 0; }