 Thus, if the two piles consist of "x" and "y" stones, where "x" is larger than "y", the next player can reduce the larger pile from "x" stones to "x" − "my" stones, as long as the latter is a nonnegative integer.The winner is the first player to reduce one pile to zero stones.Bézout's identity states that the greatest common divisor "g" of two integers "a" and "b" can be represented as a linear sum of the original two numbers "a" and "b".