Chef and the Stones

Chef has two piles of stones with him, one has N1 stones and the other has N2 stones. Fired up by boredom, he invented a game with the two piles. Before the start of the game Chef chooses an integer m. In the j-th move: He chooses a number X[J] such that 1 ≤ X[j] ≤ M, and removes X[J] stones from both the piles (this is only possible when both the piles have ≥ X[J] stones). The number chosen m