NIMGAME  Special Nim Game
In this variant of the Nim game, a pile of N stones is placed between two players. The players take alternating turns and remove some stones. The player who takes the last stone wins.
There are two restrictions however:
 The first player has to remove between 1 and N1 stones.
 After the first move, the next player has to remove between 1 and 2·k stones, where k is the number of stones removed in the last move.
If both players play perfectly, then it is possible to determine which player will win the game. Note that during the game the game state can be described by the number of remaining stones and the number of stones which can be taken in the next move. Each game state is either a winning position or a losing position.
You have to determine for which values of N (2 ≤ N ≤ 2000) the second player has a winning strategy.
Input
There is no input for this problem.
Output
Print the values N for which the second player has a winning strategy.
Example
Output: 2 3 5 ... 1597
Obviously, the example output is incomplete and shows only the first three values and the last value to be printed.
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ALi Ibrahim:
20170417 19:05:36
Awesome problem, really really enjoined solving it :D


b_aditya:
20170102 06:47:49
Last edit: 20170102 06:50:43 

jkelava6:
20150629 12:55:18
Last edit: 20150629 13:02:24 
Added by:  Adrian Kuegel 
Date:  20070118 
Time limit:  0.833s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 