package main import ( "bufio" "fmt" "os" "strings" ) const MDO int = 998244353 func main() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var n, k int fmt.Fscan(in, &n, &k) perm := make([]int, n) for i := 0; i < n; i++ { fmt.Fscan(in, &perm[i]) perm[i]-- } tree := NewPermutationTree() root := tree.Build(perm) dp := make([][]int, k+1) // dp[k][i] 表示将perm[0:i]分成k段的方案数 for i := 0; i <= k; i++ { dp[i] = make([]int, n+1) } dp[0][0] = 1 var dfs func(*Node) dfs = func(node *Node) { if node.IsCut() || node.IsLeaf() { for i := 0; i < k; i++ { dp[i+1][node.right] += dp[i][node.left] dp[i+1][node.right] %= MDO } } sum := make([]int, k) for _, child := range node.children { dfs(child) if node.IsJoin() { for i := 0; i < k; i++ { dp[i+1][child.right] += sum[i] dp[i+1][child.right] %= MDO sum[i] += dp[i][child.left] sum[i] %= MDO } } } } dfs(root) for i := 1; i <= k; i++ { fmt.Fprintln(out, dp[i][n]) } } type NodeType int const ( JOIN_ASC NodeType = iota JOIN_DESC LEAF CUT ) type Node struct { kind NodeType left, right int // [left, right) => 顶点对应的区间 minV, maxV int // [minV, maxV) => 顶点对应的区间中的最小值和最大值 children []*Node } func (n *Node) String() string { mp := map[NodeType]string{ JOIN_ASC: "JOIN_ASC", JOIN_DESC: "JOIN_DESC", LEAF: "LEAF", CUT: "CUT", } sb := []string{"Node:\n"} sb = append(sb, fmt.Sprintf("kind : %v\n", mp[n.kind])) sb = append(sb, fmt.Sprintf("left && right : [%v, %v)\n", n.left, n.right)) sb = append(sb, fmt.Sprintf("minV && maxV : [%v, %v)\n", n.minV, n.maxV)) sb = append(sb, fmt.Sprintf("childrenCount : %v", len(n.children))) return strings.Join(sb, " ") } func (n *Node) Size() int { return n.right - n.left } func (n *Node) IsJoin() bool { return n.kind == JOIN_ASC || n.kind == JOIN_DESC } func (n *Node) IsLeaf() bool { return n.kind == LEAF } func (n *Node) IsCut() bool { return n.kind == CUT } type PermutationTree struct{ Root *Node } func NewPermutationTree() *PermutationTree { return &PermutationTree{} } func (pt *PermutationTree) Build(nums []int) *Node { n := len(nums) desc, asc := []int{-1}, []int{-1} st := []*Node{} seg := newRangeAddRangeMin(make([]int, n)) for i := 0; i < n; i++ { for desc[len(desc)-1] != -1 && nums[i] > nums[desc[len(desc)-1]] { seg.Update(desc[len(desc)-2]+1, desc[len(desc)-1]+1, nums[i]-nums[desc[len(desc)-1]]) desc = desc[:len(desc)-1] } for asc[len(asc)-1] != -1 && nums[i] < nums[asc[len(asc)-1]] { seg.Update(asc[len(asc)-2]+1, asc[len(asc)-1]+1, nums[asc[len(asc)-1]]-nums[i]) asc = asc[:len(asc)-1] } desc = append(desc, i) asc = append(asc, i) t := &Node{kind: LEAF, left: i, right: i + 1, minV: nums[i], maxV: nums[i] + 1} for { kind := CUT if len(st) > 0 { if st[len(st)-1].maxV == t.minV { kind = JOIN_ASC } else if t.maxV == st[len(st)-1].minV { kind = JOIN_DESC } } if kind != CUT { r := st[len(st)-1] if kind != r.kind { r = &Node{kind: kind, left: r.left, right: r.right, minV: r.minV, maxV: r.maxV, children: []*Node{r}} } pt.addChild(r, t) st = st[:len(st)-1] t = r } else if seg.Query(0, i+1-t.Size()) == 0 { t = &Node{kind: CUT, left: t.left, right: t.right, minV: t.minV, maxV: t.maxV, children: []*Node{t}} // do while for { pt.addChild(t, st[len(st)-1]) st = st[:len(st)-1] if t.maxV-t.minV == t.Size() { break } } for i, j := 0, len(t.children)-1; i < j; i, j = i+1, j-1 { t.children[i], t.children[j] = t.children[j], t.children[i] } } else { break } } st = append(st, t) seg.Update(0, i+1, -1) } pt.Root = st[0] return st[0] } func (pt *PermutationTree) addChild(t, c *Node) { t.children = append(t.children, c) t.left = min(t.left, c.left) t.right = max(t.right, c.right) t.minV = min(t.minV, c.minV) t.maxV = max(t.maxV, c.maxV) } func min(a, b int) int { if a < b { return a } return b } func max(a, b int) int { if a > b { return a } return b } const INF int = 1e18 type rangeAddRangeMin struct { n, head int rangeMin, rangeAdd []int } func newRangeAddRangeMin(nums []int) *rangeAddRangeMin { res := &rangeAddRangeMin{} res.n = len(nums) res.head = 1 for res.head < res.n { res.head <<= 1 } res.rangeMin, res.rangeAdd = make([]int, res.head*2), make([]int, res.head*2) for i := range res.rangeMin { res.rangeMin[i] = INF } copy(res.rangeMin[res.head:], nums) for i := res.head - 1; i > 0; i-- { res.merge(i) } return res } func (r *rangeAddRangeMin) Update(start, end, add int) { r.update(start, end, 1, 0, r.head, add) } func (r *rangeAddRangeMin) Query(start, end int) int { return r.query(start, end, 1, 0, r.head) } func (r *rangeAddRangeMin) Get(pos int) int { return r.Query(pos, pos+1) } func (r *rangeAddRangeMin) query(start, end, pos, left, right int) int { if right <= start || end <= left { return INF } if start <= left && right <= end { return r.rangeMin[pos] + r.rangeAdd[pos] } return min(r.query(start, end, pos*2, left, (left+right)/2), r.query(start, end, pos*2+1, (left+right)/2, right)) + r.rangeAdd[pos] } func (r *rangeAddRangeMin) update(start, end, pos, left, right, add int) { if right <= start || end <= left { return } if start <= left && right <= end { r.rangeAdd[pos] += add return } r.update(start, end, pos*2, left, (left+right)/2, add) r.update(start, end, pos*2+1, (left+right)/2, right, add) r.merge(pos) } func (r *rangeAddRangeMin) merge(pos int) { r.rangeMin[pos] = min(r.rangeMin[pos*2]+r.rangeAdd[pos*2], r.rangeMin[pos*2+1]+r.rangeAdd[pos*2+1]) }