147. Pick up stones

There is a pile of n (n > 0) stones.

Player A and Player B take turns to pick 1 or 2 stones from the pile. A starts first.

Who picks the last stone loses the game.

Now here is the question, is there a winning strategy for A or B ? If so, returns the player name. If there is none, return null.

winningStonePicking(1)
// 'B'

winningStonePicking(2)
// 'A'

winningStonePicking(3)
// 'A'

winningStonePicking(4)
// 'B'