By Monirul Hasan Tomal, Southeast University Bangladesh
The Fibonacci number is defined by the following recurrence:
But we're not interested in the Fibonacci numbers here. We would like to know how many calls does it take to evaluate the n Fibonacci number if we follow the given recurrence. Since the numbers are going to be quite large, we'd like to make the job a bit easy for you. We'd only need the last digit of the number of calls, when this number is represented in base b.
Input consists of several test cases. For each test there will be two integers n (0 ≤ n < (2^{63} - 1)) and b (1 < b ≤ 10000). Input is terminated by a test case where n=0 and b=0, you must not process this test case.
For each test case, print the number of test case first. Then print n, b and the last digit (in base b) of the number of calls. There should be a single space between the two numbers of a line. Note that the last digit has to be represented in decimal number system.
Input Sample | Output Sample |
0 100 |
Case 1: 0 100 1 |