DMOPC '15 Contest 7 P4 - Magic - Olympiads Online Judge

DMOPC '15 Contest 7 P4 - Magic

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Points: 10 (partial)

Time limit: 0.6s

Memory limit: 64M

Author:

WallE256

Problem types

Two magicians named Alice and Bob participate in a challenge. The two participate in a race on a circular track split into $K$ ~K~ equal-length sectors, determined by the points $P_0, P_1, \dots, P_{K-1}$ ~P_0, P_1, \dots, P_{K-1}~.

Alice starts at point $P_a$ ~P_a~ and runs through $S_a$ ~S_a~ sectors per second.
Bob starts at point $P_b$ ~P_b~ and runs through $S_b$ ~S_b~ sectors per second.

If at any point in the race the distance between the two is less than $D$ ~D~, 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 $D$ ~D~. 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 $P_0$ ~P_0~ and Bob to $P_0$ ~P_0~ is prime.
Bob wins if Alice cannot.

In a given scenario, who wins?

Input Specification

The first line of input will contain the integers $K$ ~K~ $(0 < K \le 1000)$ ~(0 < K \le 1000)~ and $D$ ~D~ $(0 \le D < \dfrac{K}{2})$ ~(0 \le D < \dfrac{K}{2})~.
The second line of input will contain the integers $S_a$ ~S_a~ and $S_b$ ~S_b~.
The third line of input will contain the integers $P_a$ ~P_a~ and $P_b$ ~P_b~.

Output Specification

Either Alice or Bob, identifying the winner.

Constraints

$S_a, S_b, P_a, P_b < K$ ~S_a, S_b, P_a, P_b < K~.
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 $(\text{Alice}, \text{Bob})$ ~(\text{Alice}, \text{Bob})~ are $(0,1)$ ~(0,1)~, but immediately this changes to $(0, 2)$ ~(0, 2)~ as Alice pushes Bob. In the second instant, we have the positions $(0+2=2, 2+3=5)$ ~(0+2=2, 2+3=5)~, such that the sum of distances to $P_0$ ~P_0~ is $(6-2)+(6-5)=5$ ~(6-2)+(6-5)=5~. Since $5$ ~5~ is a prime number, Alice wins.

Comments

0

kobortor commented on April 14, 2016, 12:47 a.m. ← edited →

When the position is $(0, 2)$ ~(0, 2)~, why doesn't she win?

0

bobbotboy commented on April 14, 2016, 12:57 a.m. ← edited →

Constraints: At least a turn is executed.

I think this means that each person must move once (by $S_a$ ~S_a~ and $S_b$ ~S_b~ units) before calculamatating whether prime or not.

1

kobortor commented on April 14, 2016, 1:06 a.m.

Then the testcase is weak, I submitted without checking if its the first run and got AC.

1
d commented on April 12, 2016, 9:11 p.m. ← edited →
100 2 35 2 0 10

Edit: Alice and Bob don't really run in a continuous motion, they teleport $S$ ~S~ sectors every second.