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.List
import qualified Data.Vector.Unboxed as V

main = do
  x:y:_ <- map read . words <$> getLine :: IO [Int]
  putStrLn $ show $ path x y

path :: Int -> Int -> Int
path x y | mod (x+y) 3 /= 0 = 0
         | otherwise = let n = div (x+y) 3 in
                       if (x-n) < 0 || (y-n) < 0 then 0
                       else cmb n (x-n)

cmb n r = cmbMemo n V.! r
    where cmbMemo :: Int -> V.Vector Int
          cmbMemo 1 = V.fromList [1,1]
          cmbMemo n =
              let memo = cmbMemo (n-1) in
              V.fromList
                   [ mod ((if r == 0 then 0 else memo V.! (r-1)) + (if r == n then 0 else memo V.! r)) 1000000007
                   | r <- [0..n] ]