CF78C Beaver Game

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• 评测方式 RemoteJudge
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• 难度 普及+/提高
• 时空限制 1000ms / 256MB
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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.

输入样例#1： 复制
1 15 4

输出样例#1： 复制
Timur
输入样例#2： 复制
4 9 5

输出样例#2： 复制
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.

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