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.

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 $1000000$ 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.

-----Examples-----
Sample Input:
BABA
Sample Output:
2
0
1

Source: kattis | Difficulty: MEDIUM


Solutions: