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: Accepted)

import Control.Applicative
import Control.Monad
import Data.Functor
import Data.List
import Data.Maybe

base = 10 ^ 9 + 7

mmul x y = (x * y) `mod` base
mpow x 0 = 1
mpow x y
  | odd y  = mmul x $ mmul t t
  | even y = mmul t t
  where
    t = mpow x $ div y 2

minv = flip mpow (base - 2)

c n k
  | k == 0 || k==n   = 1
  | k<0 || k > n     = 0
  | otherwise        = mmul (foldl1 mmul [n-k+1..n]) (foldl1 mmul $ map minv [1..k])

f x y
  | q /= 0 = 0
  | x < p = 0
  | y < p = 0
  | otherwise = c p (min x y - p)
  where
    (p, q) = divMod (x + y) 3

main = map read . words <$> getLine >>= \[x, y] -> print $ f x y