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)

modIntDivisor :: Int
modIntDivisor = floor 1e9 + 7

extGcd :: Integral a => Int -> Int -> (Int, Int)
extGcd a 0 = (1, 0)
extGcd a b = (x, y)
	where
		(x', y') = extGcd b (a `mod` b)
		x = y'
		y = x' - a `div` b * y';

newtype ModInt = ModInt { unModInt :: Int } deriving (Eq, Show)

modInt :: Int -> ModInt
modInt x = ModInt $ (x `mod` modIntDivisor + modIntDivisor) `mod` modIntDivisor

modIntMap2 :: (Int -> Int -> Int) -> ModInt -> ModInt -> ModInt
modIntMap2 f a b = modInt $ f (unModInt a) (unModInt b)

instance Num ModInt where
	(+) = modIntMap2 (+)
	(-) = modIntMap2 (-)
	(*) = modIntMap2 (*)
	abs = id
	signum _ = 1
	fromInteger = modInt . fromInteger

instance Enum ModInt where
	toEnum = modInt
	fromEnum = unModInt

minv :: ModInt -> ModInt
minv a = modInt y
	where (_, y) = extGcd modIntDivisor $ unModInt a

mdiv :: ModInt -> ModInt -> ModInt
mdiv x y = x * minv y

mperm :: ModInt -> ModInt -> ModInt
mperm _ 0 = 1
mperm n r = product [(n - r + 1)..n]

mcomb :: ModInt -> ModInt -> ModInt
mcomb n r = mperm n r `mdiv` product [1..r]

calc :: Int -> Int -> ModInt
calc x y
	| (x + y) `mod` 3 /= 0       = 0
	| (diff + dist) `mod` 2 /= 0 = 0
	| n < 0 || dist < n          = 0
	| otherwise = mcomb (modInt dist) (modInt n)
	where
		diff = x - y
		dist = (x + y) `div` 3
		n = (diff + dist) `div` 2

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