Diana is going to write a list of all positive integers between $A$ and $B$, inclusive, in base $10$ and
without any leading zeros. She wants to know how many times each digit is going to be used.

Each test case is given in a single line that contains two integers $A$ and $B$ $(1 \leq A \leq B \leq 10^8)$.

The last test case is followed by a line containing two zeros.

For each test case output a single line with $10$ integers representing the number of times each digit is used when writing all integers between $A$ and $B$, inclusive, in base $10$ and without leading zeros. Write the counter for each digit in increasing order from $0$ to $9$.

Input

1 9
12 321
5987 6123
12345678 12345679
0 0

Output

0 1 1 1 1 1 1 1 1 1
61 169 163 83 61 61 61 61 61 61
134 58 28 24 23 36 147 24 27 47
0 2 2 2 2 2 2 2 1 1