P3480 [POI 2009] KAM-Pebbles

Johny and Margaret are playing "pebbles". Initially there is a certain number of pebbles on a table, grouped in $n$ piles. The piles are next to each other, forming a single row. The arrangement of stones satisfies an additional property that each pile consists of at least as many pebbles as the one to the left (with the obvious exception of the leftmost pile). The players alternately remove any number of pebbles from a single pile of their choice. They have to take care, though, not to make any pile smaller than the one left to it. In other words, the piles have to satisfy the initial property after the move as well. When one of the players cannot make a move (i.e. before his move there are no more pebbles on the table), he loses. Johny always starts, to compensate for Margaret's mastery in this game. In fact Margaret is so good that she always makes the best move, and wins the game whenever she has a chance. Therefore Johny asks your help - he would like to know if he stands a chance of beating Margaret with a particular initial arrangement. Write a programme that determines answers to Johny's inquiries.

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