Alice&Brown
问题 D:
时间限制: 1 Sec 内存限制: 128 MB
提交: 50 解决: 35
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题目描述
Alice and Brown loves games. Today, they will play the following game.
In this game, there are two piles initially consisting of X and Y stones, respectively. Alice and Bob alternately perform the following operation, starting from Alice:
Take 2i stones from one of the piles. Then, throw away i of them, and put the remaining i in the other pile. Here, the integer i (1≤i) can be freely chosen as long as there is a sufficient number of stones in the pile.
The player who becomes unable to perform the operation, loses the game.
Given X and Y, determine the winner of the game, assuming that both players play optimally.
Constraints
0≤X,Y≤1018
In this game, there are two piles initially consisting of X and Y stones, respectively. Alice and Bob alternately perform the following operation, starting from Alice:
Take 2i stones from one of the piles. Then, throw away i of them, and put the remaining i in the other pile. Here, the integer i (1≤i) can be freely chosen as long as there is a sufficient number of stones in the pile.
The player who becomes unable to perform the operation, loses the game.
Given X and Y, determine the winner of the game, assuming that both players play optimally.
Constraints
0≤X,Y≤1018
输入
Input is given from Standard Input in the following format:
X Y
X Y
输出
Print the winner: either Alice or Brown.
样例输入
2 1
样例输出
Brown
提示
Alice can do nothing but taking two stones from the pile containing two stones. As a result, the piles consist of zero and two stones, respectively. Then, Brown will take the two stones, and the piles will consist of one and zero stones, respectively. Alice will be unable to perform the operation anymore, which means Brown's victory.
//推导结果：若X，Y相差小于等于1 Brown胜 否则Alice胜
X,Y相差大于1时 可以通过一步 使X，Y相差小于等于1
转化为X，Y相差小于等于1时谁获胜的问题
