You are given two ints: a and b.
You are now going to perform a sequence of zero or more steps.
In each step you will double one of the integers and increment the other.
Your goal is to reach a state in which both integers have the same value.
More precisely, in each step you will perform one of the following two moves:
- Move '0': add 1 to a, multiply b by 2
- Move '1': multiply a by 2, add 1 to b
Any sequence of steps can now be written as a string of zeros and ones.
It is guaranteed that for each pair a, b that satifies the constraints (given below) it is possible to reach the goal in at most 2500 steps.
Find any such sequence of steps and return a String containing its description.
Note that your solution does not have to minimize the number of steps.
Any valid solution that consists of at most 2500 steps will be accepted.