MathDB

Fedir and Mykhailo have three piles of stones: the first contains

100

stones, the second

101

, the third

102

. They are playing a game, going in turns, Fedir makes the first move. In one move player can select any two piles of stones, let's say they have

a

and

b

stones left correspondently, and remove

gcd(a, b)

stones from each of them. The player after whose move some pile becomes empty for the first time wins. Who has a winning strategy?
As a reminder,

gcd(a, b)

denotes the greatest common divisor of

a, b

.
(Proposed by Oleksii Masalitin)

Problem Statement