Diana is going to write a list of all positive integers between and , inclusive, in base 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 and (1 \le A \le B \le 10^8).
The last test case is followed by a line containing two zeros.
For each test case output a single line with integers representing the number of times each digit is used when writing all integers between and , inclusive, in base and without leading zeros. Write the counter for each digit in increasing order from to .
Example 1