The Counting Problem

You are given two integers $a$ and $b$. List every integer between $a$ and $b$, inclusive, and count how many times each digit (0 through 9) appears across the whole list.

For example, if $a = 1024$ and $b = 1032$, the list is

1024 1025 1026 1027 1028 1029 1030 1031 1032

which contains the digit 0 ten times, the digit 1 ten times, the digit 2 seven times, the digit 3 three times, and so on.

The order of $a$ and $b$ is not fixed: $a$ may be greater than $b$, and in that case you still count every integer between the two values.

The input consists of up to 500 lines. Each line contains two integers $a$ and $b$ with $0 < a, b < 100{,}000{,}000$. The input is terminated by a line containing 0 0, which is not part of the input.

For each input line, print one line with ten integers separated by single spaces. The first integer is the number of occurrences of the digit 0, the second is the number of occurrences of the digit 1, and so on, up to the tenth integer, which is the number of occurrences of the digit 9.