Game theory -3 problem

sample input

2
2
4 2
3
5 2 3

how second player is winning.
i think first player is winning.

The second player wins if we consider the following moves :-
Player 1 breaks down 4 into 2 piles of 2 -> 2 2 2
Player 2 breaks down 2 into 2 piles of 1 -> 1 1 2 2
Player 1 breaks down 2 into 2 piles of 1 -> 1 1 1 1 2
Player 2 breaks down 2 into 2 piles of 1 -> 1 1 1 1 1 1

Player 1 now has no move therefore he loses.

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