Nim Game Problem (Game is Love) with Solution

Let's say two players (p1, p2) are playing a game, in which they have two piles of stones N1 and N2. They take a turns by picking any even positive number of piles and keep half of them on other piles and throw another half. Whoever can not make a move loses. p1 makes the first move. Consider that both players will play optimized. 

(Level: Hard)

INPUT: N1 = 3 and N2 = 6

OUTPUT: p1 wins just (just print--> p1)

EXPLANATION: 

3 6 --- This is the case

4 4 --- move made by p1

2 5 --- move made by p2

3 3 --- move made by p1

1 4 --- move made by p2

2 2 --- move made by p1

1 3 --- move made by p2

2 1 --- move made by p1

0 2 --- move made by p2

1 0 --- move made by p1

Now as you can see, there is nothing to move (for p2) so that p1 win's the game.

Here is the solution in python : 

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