P16157 [ICPC 2016 NAIPC] K-Inversions

You are given a string $s$ consisting only of upper case letters **A** and **B**. For an integer $k$, a pair of indices $i$ and $j$ ($1 \leq i < j \leq n$) is called a $k$-inversion if and only if $s[i] = \text{B}$, $s[j] = \text{A}$ and $j - i = k$. Consider the string **BABA**. It has two 1-inversions and one 3-inversion. It has no 2-inversions. :::align{center}  ::: For each $k$ between $1$ and $n-1$ (inclusive), print the number of $k$-inversions in the string $s$.

Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. The input will consist of a single line with a string $s$, which consists of only upper case **A**s and **B**s. The string $s$ will be between $1$ and $1,000,000$ characters long. There will be no spaces.

Output $n-1$ lines, each with a single integer. The first line’s integer should be the number of 1-inversions, the second should be the number of 2-inversions, and so on.