Solving Problem , I got recurrence as f(n)= @f((n+1)/2) + @f(n-1) ,here @ denotes negation, f(x) is 0 if player with x stones loose and 1 if player left with x stones wins.As n can be high as 10¹⁸ so matrix exponentiation would do this,

| @ @ | x | f(n) | = | f(n+1) |
| 1 0 | | f(n/2+1) | | f(n) |

but I am unable to do algebra with this @ operation.