Coin game winner where every player has three choices

A and B are playing a game. In the beginning, there are n coins. Given two more numbers x and y. In each move, a player can pick x or y or 1 coin. A always starts the game. The player who picks the last coin wins the game or the person who is not able to pick any coin loses the game. For a given value of n, find whether A will win the game or not if both are playing optimally.

Examples: 

Input : n = 5, x = 3, y = 4
Output : A
There are 5 coins, every player can pick 1 or
3 or 4 coins on his/her turn.
A can win by picking 3 coins in first chance.
Now 2 coins will be left so B will pick one 
coin and now A can win by picking the last coin.

Input : 2 3 4
Output : B

Let us take few example values of n for x = 3, y = 4. 
n = 0 A can not pick any coin so he losses 
n = 1 A can pick 1 coin and win the game 
n = 2 A can pick only 1 coin. Now B will pick 1 coin and win the game 
n = 3 4 A will win the game by picking 3 or 4 coins 
n = 5, 6 A will choose 3 or 4 coins. Now B will have to choose from 2 coins so A will win.
We can observe that A wins game for n coins only when B loses for coins n-1 or n-x or n-y. 

A

Time Complexity: O(n)
Auxiliary Space: O(n)