A8112. Beaver Game
编程题
普及/提高-
知识点
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.
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 #1
1 15 4
输出 #1
Timur
输入 #2
4 9 5
输出 #2
Marsel
说明/提示
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.
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.