Digits Count#3748

Digits Count

1 second
64 megabytes
Very easy

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.

Input

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.

Output

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 .

Examples

Example 1

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