Given two positive integers $a$ and $b$, find the number of occurrences of each digit ($0-9$) in all integers in the range $[a, b]$.

Input

The input contains a single line with two integers $a$ and $b$, as described above.

Output

The output contains a single line with 10 integers, representing the number of times each digit from $0$ to $9$ appears in the range $[a, b]$, respectively.

Examples

Input 1

1 99

Output 1

9 20 20 20 20 20 20 20 20 20

Constraints

For $30\%$ of the data, $a \le b \le 10^6$. For $100\%$ of the data, $a \le b \le 10^{12}$.