A Heap of Heaps

You are given a sequence of n integers $a_1, a_2, \dots, a_n$. Take the sequence as the node values of a k-ary heap and count the nodes that break the min-heap property.

A k-ary heap is a rooted tree in which an internal node has at most k children. The nodes are numbered 1 to n and node 1 is the root. Node v has nodes $k(v-1)+2$, $k(v-1)+3$, $\dots$, $kv+1$ as its children. A child whose number is greater than n does not exist, so only the last internal node can have fewer than k children.

Let $p(v)$ be the parent of a node v that is not the root. Node v breaks the min-heap property when $a_v < a_{p(v)}$. For each $k = 1, 2, \dots, n-1$, count the nodes that break the property.

The first line contains an integer n ($1 \le n \le 200000$).

The second line contains the n integers $a_1, a_2, \dots, a_n$ of the sequence, separated by spaces ($-10^9 \le a_i \le 10^9$).

Print $n-1$ integers on one line, separated by single spaces. The $i$-th number is the count of nodes that break the min-heap property in the $i$-ary heap. When $n = 1$ there is no such k, so print nothing.

The pictures below show the heaps for $k = 1, 2, 3, 4$ when $n = 5$ and the sequence is $1\ 5\ 4\ 3\ 2$. The red nodes break the min-heap property.