Two magicians named Alice and Bob participate in a challenge. The two participate in a race on a circular track split in equal-length sectors, determined by the points .
- Alice starts at point and runs through sectors per second.
- Bob starts at point and runs through sectors per second.
If at any point in the race the distance between the two is less than , Alice will use her magic to instantly push Bob a minimum distance such that the two magicians remain at a distance greater or equal to . The winning conditions are as follows:
- Alice wins if it is possible that sometime during the race, the sum of the shortest distance (running on the circular track) between herself to and Bob to is prime.
- Bob wins if Alice cannot.
In a given scenario, who wins?
The first line of input will contain the integers and .
The second line of input will contain the integers and .
The third line of input will contain the integers and .
Bob, identifying the winner.
- At least a turn is executed.
- In case Alice and Bob are on the same segment, Bob is pushed behind Alice.
6 2 2 3 0 1
At the start, the positions of are , but immediately this changes to as Alice pushes Bob. In the second instant, we have the positions , such that the sum of distances to is . Since is a prime number, Alice wins.