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: Time Limit Exceeded)

import Data.Int

modulus :: Int64
modulus = 10000000007

main :: IO ()
main = do
    (x,y) <- (\[a,b] -> (a,b)) . (map read . words)
        <$> getLine :: IO (Int,Int)
    let z = min x y
        s = sum [ a+b | a <- [0..z], b <- [0..z]
                , (a + 2 * b, 2 * a + b) == (x,y)]
    print $ (fromIntegral s :: Int64) `rem` modulus