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2016-04-16 17:00 UTC

NAIPC 2016

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2016-04-16 22:00 UTC
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Problem E
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 $j$ ($1 \le i<j \le n$) is called a $k$-inversion if and only if $s[i] = \textbf{B}$, $s[j] = \textbf{A}$ and $j-i = k$.

Consider the string BABA. It has two $1$-inversions and one $3$-inversion. It has no $2$-inversions.

\includegraphics{k.jpg}

For each $k$ between $1$ and $n-1$ (inclusive), print the number of $k$-inversions in the string $s$.

Input

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 As and Bs. The string $s$ will be between $1$ and $1\, 000\, 000$ characters long. There will be no spaces.

Output

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.

Sample Input 1 Sample Output 1
BABA
2
0
1
Sample Input 2 Sample Output 2
BBBBBAAAAA
1
2
3
4
5
4
3
2
1