Module: The Euler function and other problems in number theory


Problem

4 /9


Fast exponentiation

Problem

Raising to a power is much faster than n multiplications! To do this, use the following recurrence relations:

\(a^n=(a^2)^{n/2}\)  even n,  
\(a^n=a \cdot a^{n-1}\)  for odd n.
 
Implement the fast exponentiation algorithm. If you do everything right, then the complexity of your algorithm will be O(logn) .
 
Input
Enter a real number a and an integer n.
 
Imprint 
Print the answer to the problem, with an accuracy of 6 decimal places.
 
You can't use standard exponentiation.
 

 

Examples
# Input Output
1 2
7
128
2
1.00001
100000
2.71827