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: Runtime Error)

fact 0 = 1
fact n = (n*fact (n-1))

product' [] = 1
product' (x:xs) = (x*product' xs)`mod`(10^9 + 7)

main :: IO ()
main = do
  l1 <- getLine
  let [x, y] = map read $ words l1 :: [Integer]
      (x', y') = (max x y, min x y)
      n = x' - y' -- (y'-n, y'-n)から(x, y)への移動回数
      m = (y' - n)`div`3 -- (y'-n, y'-n)への移動回数/2
      k = m + n
  if y'*2 < x' || (x + y) `mod` 3 /= 0 then
    print 0
  else
    print $ (product' (f (drop (fromIntegral k) [1..m+k]) [1..m]))`mod`(10^9 + 7)

f ys [] = ys
f (y:ys) (x:xs)
  | y`mod`x /= 0 = y:f ys (x:xs)
  | otherwise = f ((y`div`x):ys) xs