Problem E |
Super Lucky Numbers |
Time Limit |
2 Seconds |
Some people believe that 13 is an unlucky number. So they always want to avoid the number 13. In some buildings you will find that there is no 13^{th} floor. After 12^{th} floor there is 14^{th} floor. In a number if there is no 13 (i.e. no ‘1’ is followed by a ‘3’) then we may call it a super lucky number. For example, 12345 is a super lucky number. But if any number contains 13 then it is not a super lucky number such as 13254 or 21345. Given the number of digits N in a number and a base B, you have to find out how many super lucky numbers are possible with N digits in the base B. B should be greater than 3, as because the digit 3 is present in only for base 4 or more. Note that leading 0’s are not significant. So, 011 is not a valid three digit number.
Input
There will be several lines in the input each containing two positive integers B and N, where 4 ≤ B ≤ 128 and N ≤ 100. A pair of zero will indicate the end of input and it should not be processed.
Output
For each line in the input print the count of super lucky numbers of N digits in the base B.
Sample Input |
Output for Sample Input |
4 2 |
11 |