Kate and Emilico are playing a game. There are $3$ integers $a,b,c$. It is guaranteed that there exists a non-degenerate triangle whose side lengths are $a,b,c$ respectively. The game goes as follows. Players take turns in decreasing a certain positive integer on one of the $3$ integers. If there doesn't exist a non-degenerate triangle whose side lengths are $a,b,c$ after a player's operation, the player loses.
Kate goes first. If both of them play optimally, will Kate win?