Beaver Game
题意翻译
两只海狸(Timur and Marsel)做游戏
什么游戏呢?
有n条长度为m的木棍
从Timur开始,每只海狸轮流将一根已有的木棍任意等分
但要保证等分后的每一段长度都是不小于k的整数
(m,n,k为小于等于1000000000的正整数)
先无法等分的海狸输
已知Timur and Marsel,无比聪明,智商碾压人类(真可怕),这导致他们每一步都最优
那聪明的你,能不能告诉更聪明的评测机,到底谁会获胜呢?
贡献者:HandSome_Colin
题目描述
Two beavers, Timur and Marsel, play the following game.
There are $ n $ logs, each of exactly $ m $ meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than $ k $ meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
输入输出格式
输入格式
The first line contains three integers $ n $ , $ m $ , $ k $ ( $ 1<=n,m,k<=10^{9} $ ).
输出格式
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
输入输出样例
输入样例 #1
1 15 4
输出样例 #1
Timur
输入样例 #2
4 9 5
输出样例 #2
Marsel
说明
In the first sample the beavers only have one log, of $ 15 $ meters in length. Timur moves first. The only move he can do is to split the log into $ 3 $ parts each $ 5 $ meters in length. Then Marsel moves but he can't split any of the resulting logs, as $ k=4 $ . Thus, the winner is Timur.
In the second example the beavers have $ 4 $ logs $ 9 $ meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than $ 5 $ meters, that's why he loses instantly.