YJJ is a salesman who has traveled through western country. YJJ is always on journey. Either is he at the destination, or on the way to destination.
One day, he is going to travel from city A to southeastern city B. Let us assume that A is (0,0) on the rectangle map and B (10^9,10^9). YJJ is so busy so he never turn back or go twice the same way, he will only move to east, south or southeast, which means, if YJJ is at (x,y) now (0\leqslant x\leqslant 10^9,0\leqslant y\leqslant 10^9), he will only forward to (x+1,y), (x,y+1) or (x+1,y+1).