Interesting Game
题目描述
Two best friends Serozha and Gena play a game.
Initially there is one pile consisting of n stones on the table. During one move one pile should be taken and divided into an arbitrary number of piles consisting of a1>a2>...>ak>0 stones. The piles should meet the condition a1-a2=a2-a3=...=ak-1-ak=1. Naturally, the number of piles k should be no less than two.
The friends play in turns. The player who cannot make a move loses. Serozha makes the first move. Who will win if both players play in the optimal way?
The single line contains a single integer n (1≤n≤105).
If Serozha wins, print k, which represents the minimal number of piles into which he can split the initial one during the first move in order to win the game.
If Gena wins, print "-1" (without the quotes).
3
2
6
-1
100
8
题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 44 题。保留原作者与原赛事署名。