There is a knight - the chess piece - at the origin (0, 0) of a two-dimensional grid. When the knight is at the square (i, j), it can be moved to either (i+1,j+2) or (i+2, j+1). In how many ways can the knight reach the square (X, Y)? Find the number of ways modulo 10^9 + 7.

-----Constraints-----

• 1 \leq X \leq 10^6
• 1 \leq Y \leq 10^6
• All values in input are integers.

-----Input----- Input is given from Standard Input in the following format: X Y

-----Output----- Print the number of ways for the knight to reach (X, Y) from (0, 0), modulo 10^9 + 7.

-----Sample Input----- 3 3

-----Sample Output----- 2

There are two ways: (0,0) \to (1,2) \to (3,3) and (0,0) \to (2,1) \to (3,3).