CF1221E Game With String

Alice和Bob在玩一个游戏，最初他们有一个字符串$s_1,s_2……,s_n$,只由X和.组成。他们轮流行动，Alice先手。每一轮，玩家选择一个只由.组成的字串，将它全都改为X。Alice必须选择度为a的字串，Bob必须选择度为b的字串，保证a>b。 举个例子，如果S=...X..，a=3,b=2,那么Alice只能把它变为XXXX...，如果Bob行动可能可以变为XX.X.., .XXX.. 或 ...XXX. 谁先不能行动谁就输了。假设他们都聪明绝顶，请你来预测谁会赢。 你要回答q组询问。

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In the first query Alice can select substring $ s_3 \dots s_5 $ . After that $ s $ turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring $ s_2 \dots s_6 $ . After that $ s $ turns into .XXXXX.X..X, and Bob can't make a move after that.