#include using namespace std; using int64 = long long; // const int mod = 1e9 + 7; const int mod = 998244353; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 > &p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in: v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e: t) fill_v(e, v); } template< typename F > struct FixPoint : F { FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } /** * @brief Lazy-Segment-Tree(遅延伝搬セグメント木) * @docs docs/lazy-segment-tree.md */ template< typename Monoid, typename OperatorMonoid, typename F, typename G, typename H > struct LazySegmentTree { private: int n{}, sz{}, height{}; vector< Monoid > data; vector< OperatorMonoid > lazy; const F f; const G g; const H h; const Monoid M1; const OperatorMonoid OM0; inline void update(int k) { data[k] = f(data[2 * k + 0], data[2 * k + 1]); } inline void all_apply(int k, const OperatorMonoid &x) { data[k] = g(data[k], x); if(k < sz) lazy[k] = h(lazy[k], x); } inline void propagate(int k) { if(lazy[k] != OM0) { all_apply(2 * k + 0, lazy[k]); all_apply(2 * k + 1, lazy[k]); lazy[k] = OM0; } } public: LazySegmentTree() = default; explicit LazySegmentTree(int n, const F f, const G g, const H h, const Monoid &M1, const OperatorMonoid &OM0) : n(n), f(f), g(g), h(h), M1(M1), OM0(OM0) { sz = 1; height = 0; while(sz < n) sz <<= 1, height++; data.assign(2 * sz, M1); lazy.assign(2 * sz, OM0); } explicit LazySegmentTree(const vector< Monoid > &v, const F f, const G g, const H h, const Monoid &M1, const OperatorMonoid &OM0) : LazySegmentTree(v.size(), f, g, h, M1, OM0) { build(v); } void build(const vector< Monoid > &v) { assert(n == (int) v.size()); for(int k = 0; k < n; k++) data[k + sz] = v[k]; for(int k = sz - 1; k > 0; k--) update(k); } void set(int k, const Monoid &x) { k += sz; for(int i = height; i > 0; i--) propagate(k >> i); data[k] = x; for(int i = 1; i <= height; i++) update(k >> i); } Monoid get(int k) { k += sz; for(int i = height; i > 0; i--) propagate(k >> i); return data[k]; } Monoid operator[](int k) { return get(k); } Monoid prod(int l, int r) { if(l >= r) return M1; l += sz; r += sz; for(int i = height; i > 0; i--) { if(((l >> i) << i) != l) propagate(l >> i); if(((r >> i) << i) != r) propagate((r - 1) >> i); } Monoid L = M1, R = M1; for(; l < r; l >>= 1, r >>= 1) { if(l & 1) L = f(L, data[l++]); if(r & 1) R = f(data[--r], R); } return f(L, R); } Monoid all_prod() const { return data[1]; } void apply(int k, const OperatorMonoid &x) { k += sz; for(int i = height; i > 0; i--) propagate(k >> i); data[k] = g(data[k], x); for(int i = 1; i <= height; i++) update(k >> i); } void apply(int l, int r, const OperatorMonoid &x) { if(l >= r) return; l += sz; r += sz; for(int i = height; i > 0; i--) { if(((l >> i) << i) != l) propagate(l >> i); if(((r >> i) << i) != r) propagate((r - 1) >> i); } { int l2 = l, r2 = r; for(; l < r; l >>= 1, r >>= 1) { if(l & 1) all_apply(l++, x); if(r & 1) all_apply(--r, x); } l = l2, r = r2; } for(int i = 1; i <= height; i++) { if(((l >> i) << i) != l) update(l >> i); if(((r >> i) << i) != r) update((r - 1) >> i); } } template< typename C > int find_first(int l, const C &check) { if(l >= n) return n; l += sz; for(int i = height; i > 0; i--) propagate(l >> i); Monoid sum = M1; do { while((l & 1) == 0) l >>= 1; if(check(f(sum, data[l]))) { while(l < sz) { propagate(l); l <<= 1; auto nxt = f(sum, data[l]); if(not check(nxt)) { sum = nxt; l++; } } return l + 1 - sz; } sum = f(sum, data[l++]); } while((l & -l) != l); return n; } template< typename C > int find_last(int r, const C &check) { if(r <= 0) return -1; r += sz; for(int i = height; i > 0; i--) propagate((r - 1) >> i); Monoid sum = 0; do { r--; while(r > 1 and (r & 1)) r >>= 1; if(check(f(data[r], sum))) { while(r < sz) { propagate(r); r = (r << 1) + 1; auto nxt = f(data[r], sum); if(not check(nxt)) { sum = nxt; r--; } } return r - sz; } sum = f(data[r], sum); } while((r & -r) != r); return -1; } }; template< typename Monoid, typename OperatorMonoid, typename F, typename G, typename H > LazySegmentTree< Monoid, OperatorMonoid, F, G, H > get_lazy_segment_tree (int N, const F &f, const G &g, const H &h, const Monoid &M1, const OperatorMonoid &OM0) { return LazySegmentTree{N, f, g, h, M1, OM0}; } template< typename Monoid, typename OperatorMonoid, typename F, typename G, typename H > LazySegmentTree< Monoid, OperatorMonoid, F, G, H > get_lazy_segment_tree (const vector< Monoid > &v, const F &f, const G &g, const H &h, const Monoid &M1, const OperatorMonoid &OM0) { return LazySegmentTree{v, f, g, h, M1, OM0}; } struct PermutationTree { public: enum NodeType { JOIN_ASC, JOIN_DESC, LEAF, CUT }; struct Node { NodeType type; int l, r; // [l, r) int min_v, max_v; // [min_v, max_v) vector< Node * > ch; size_t size() const { return r - l; } bool is_join() const { return type == JOIN_ASC or type == JOIN_DESC; }; bool is_leaf() const { return type == LEAF; } bool is_cut() const { return type == CUT; } }; using NP = Node *; PermutationTree() = default; private: static void add_child(NP t, NP c) { t->ch.emplace_back(c); t->l = min(t->l, c->l); t->r = max(t->r, c->r); t->min_v = min(t->min_v, c->min_v); t->max_v = max(t->max_v, c->max_v); } public: static NP build(vector< int > &A) { int n = (int) A.size(); vector< int > desc{-1}; // A[desc[0]]>A[desc[1]]>... vector< int > asc{-1}; // A[asc[0]] st; auto f = [](int a, int b) { return min(a, b); }; auto g = [](int a, int b) { return a + b; }; constexpr int lim = (1 << 30) - 1; auto seg = get_lazy_segment_tree(vector< int >(n), f, g, g, lim, 0); for(int i = 0; i < n; i++) { while(~desc.back() and A[i] > A[desc.back()]) { seg.apply(desc[desc.size() - 2] + 1, desc.back() + 1, A[i] - A[desc.back()]); desc.pop_back(); } while(~asc.back() and A[i] < A[asc.back()]) { seg.apply(asc[asc.size() - 2] + 1, asc.back() + 1, A[asc.back()] - A[i]); asc.pop_back(); } desc.emplace_back(i); asc.emplace_back(i); NP t = new Node{LEAF, i, i + 1, A[i], A[i] + 1, {}}; for(;;) { NodeType type = CUT; if(not st.empty()) { if(st.back()->max_v == t->min_v) { type = JOIN_ASC; } else if(t->max_v == st.back()->min_v) { type = JOIN_DESC; } } if(type != CUT) { NP r = st.back(); if(type != r->type) { r = new Node{type, r->l, r->r, r->min_v, r->max_v, {r}}; } add_child(r, t); st.pop_back(); t = r; } else if(seg.prod(0, i + 1 - (int) t->size()) == 0) { t = new Node{CUT, t->l, t->r, t->min_v, t->max_v, {t}}; do { add_child(t, st.back()); st.pop_back(); } while(t->max_v - t->min_v != t->size()); reverse(begin(t->ch), end(t->ch)); } else { break; } } st.emplace_back(t); seg.apply(0, i + 1, -1); } return st[0]; } }; /** * @brief Montgomery ModInt */ template< uint32_t mod, bool fast = false > struct MontgomeryModInt { using mint = MontgomeryModInt; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for(i32 i = 0; i < 4; i++) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(r * mod == 1, "invalid, r * mod != 1"); static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); u32 x; MontgomeryModInt() : x{} {} MontgomeryModInt(const i64 &a) : x(reduce(u64(fast ? a : (a % mod + mod)) * n2)) {} static constexpr u32 reduce(const u64 &b) { return u32(b >> 32) + mod - u32((u64(u32(b) * r) * mod) >> 32); } mint &operator+=(const mint &p) { if(i32(x += p.x - 2 * mod) < 0) x += 2 * mod; return *this; } mint &operator-=(const mint &p) { if(i32(x -= p.x) < 0) x += 2 * mod; return *this; } mint &operator*=(const mint &p) { x = reduce(u64(x) * p.x); return *this; } mint &operator/=(const mint &p) { *this *= p.inverse(); return *this; } mint operator-() const { return mint() - *this; } mint operator+(const mint &p) const { return mint(*this) += p; } mint operator-(const mint &p) const { return mint(*this) -= p; } mint operator*(const mint &p) const { return mint(*this) *= p; } mint operator/(const mint &p) const { return mint(*this) /= p; } bool operator==(const mint &p) const { return (x >= mod ? x - mod : x) == (p.x >= mod ? p.x - mod : p.x); } bool operator!=(const mint &p) const { return (x >= mod ? x - mod : x) != (p.x >= mod ? p.x - mod : p.x); } u32 get() const { u32 ret = reduce(x); return ret >= mod ? ret - mod : ret; } mint pow(u64 n) const { mint ret(1), mul(*this); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } mint inverse() const { return pow(mod - 2); } friend ostream &operator<<(ostream &os, const mint &p) { return os << p.get(); } friend istream &operator>>(istream &is, mint &a) { i64 t; is >> t; a = mint(t); return is; } static u32 get_mod() { return mod; } }; using modint = MontgomeryModInt< mod >; const int MOD = 998244353; using mint = MontgomeryModInt< MOD >; int main() { int N, K; cin >> N >> K; vector< int > A(N); cin >> A; for(auto &a: A) --a; using NP = PermutationTree::Node *; auto dp = make_v< mint >(K + 1, N + 1); dp[0][0] = 1; MFP([&](auto rec, NP r) -> void { if(r->is_cut() or r->is_leaf()) { for(int k = 0; k < K; k++) { dp[k + 1][r->r] += dp[k][r->l]; } } vector< modint > sum(K); for(auto &c: r->ch) { rec(c); if(r->is_join()) { for(int k = 0; k < K; k++) { dp[k + 1][c->r] += sum[k]; sum[k] += dp[k][c->l]; } } } })(PermutationTree::build(A)); for(int i = 1; i <= K; i++) { cout << dp[i][N] << "\n"; } }