JOIN

 Problem Statement

Problem Statement for DoubleOrOne

### Problem Statement

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.

### Definition

 Class: DoubleOrOne Method: findSequence Parameters: int, int Returns: String Method signature: String findSequence(int a, int b) (be sure your method is public)

### Notes

-The fact that a and b are given as ints does not imply any upper bound on their values. For example, if you start with a=1 and perform move '1' exactly 1000 times, you will have a=2^1000.

### Constraints

-a,b will be between 0 and 100, inclusive.

### Examples

0)

 `1` `1`
`Returns: ""`
 Nothing needs to be done here.
1)

 `1` `2`
`Returns: "11"`
 One way to make a,b equal is to apply move '1' twice. In this case, we get the following sequence: (1,2) -> (2,3) -> (4,4).
2)

 `2` `1`
`Returns: "1110100"`
 This example is the same as Example 1, only with a and b swapped. Here we intentionally show a different correct sequence of steps. Note that the answer "00" would also be accepted.
3)

 `10` `24`
`Returns: "001101011"`
 (10, 24) -> (11, 48) -> (12, 96) -> (24, 97) -> (48, 98) -> (49, 196) -> (98, 197) -> (99, 394) -> (198, 395) -> (396, 396)
4)

 `0` `64`
`Returns: "10111101111"`
5)

 `67` `25`
`Returns: "11111101111100000001101000000"`

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This problem was used for:
2015 TopCoder Open Algorithm Semi Final - Division I, Level Three