Hello, I'm Capricornian. I have a problem, which seems to be easy, but I have no idea how to achieve a solution of that problem in approriate time limit.

Can you help me to figure it out and find how it works?

This is the problem statement:

Number Distribution

Giving two integers A and B (A and B is in range [0..2E9]) and a non-negative integer T < 1E18.

In one operation, this rule is followed :

if (A < B) A = 2 * A, B = B - A;
else B = 2 * B, A = A - B;

Calculate A and B after T operations. (I have figured out that if you do these sequences of operation enough times, you will get back A and B in the beginning case, but I can't find the rule behind that).

Thanks for helping !

Capricornian.