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)

mo=10^9+7
main=do
 [x,y]<-map read.words<$>getLine
 let n=div(2*y-x)3
 let m=div(2*x-y)3
 print$if mod(x+y)3==0 then c(n+m)n 1 1 else 0
c a 0 x y=x*(power y$mo-2)`mod`mo
c a b x y=c(a-1)(b-1)(x*a`mod`mo)(y*b`mod`mo)
power a n
 |n==0=1
 |n`mod`2==0=power(a*a`mod`mo)(div n 2)
 |True=a*(power(a*a`mod`mo)(div n 2))`mod`mo