Problem:
Score : 400 points

Problem Statement

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 1

3 3

Sample Output 1

2

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

Sample Input 2

2 2

Sample Output 2

0

The knight cannot reach (2,2).

Sample Input 3

999999 999999

Sample Output 3

151840682

Print the number of ways modulo 10^9 + 7.

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

main :: IO ()
main = do
  [x,y] <- map (read :: String -> Integer) . words <$> getLine
  print $ ans x y

ans :: Integer -> Integer -> Integer
ans x y
  | (2*x-y) `mod` 3 /= 0   = 0
  | (2*x-y<0) || (2*y-x<0) = 0
  | otherwise = comb (s+t) s
  where
    s = (2*x-y) `div` 3
    t = (2*y-x) `div` 3

comb :: Integer -> Integer -> Integer
comb n 0 = 1
comb 0 k = 0
comb n k = (`mod` (10^9+7)) $ comb (n-1) (k-1) * n `div` k