Two magicians named Alice and Bob participate in a challenge. The two participate in a race on a circular track split into 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?
Input Specification
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
.
Output Specification
Either Alice
or Bob
, identifying the winner.
Constraints
.
- At least a turn is executed.
- In case Alice and Bob are on the same segment, Bob is pushed behind Alice.
Sample Input
6 2
2 3
0 1
Sample Output
Alice
Explanation
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.
Comments
When the position is
, why doesn't she win?
Constraints: At least a turn is executed.
I think this means that each person must move once (by
and
units) before calculamatating whether prime or not.
Then the testcase is weak, I submitted without checking if its the first run and got AC.
Edit: Alice and Bob don't really run in a continuous motion, they teleport
sectors every second.