I think ans are A and B.The important thing to note is f(k,k)=f(k,k-1+1)=f(k,k-1)-(k-1)=f(k-1+1,k-1)+1-k=f(k-1,k-1).

So,f(2000,1999)=f(1999,1999)+1999=f(1998,1998)+1999=.......=f(1,1)+1999=2001

f(1001,999)=f(1000,999)+1000=f(999,999)+1999=f(1,1)+1999=2001