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 Julia (0.5.0) (judge verdict: Runtime Error)

#=
D:
- Julia version: 
- Author: abap
- Date: 2019-11-16
=#
x,y = parse.(split(readline()))

X,Y = 0,0
for i in 1:x
    X += 2
    Y += 1
    print(X,Y)
    if (x - X)/(y - Y) == 1/2
        yoko = x
        tate = x - X
        break
    end
end
count = factorial(tate + yoko)/(factorial(tate)+factorial(yoko))
println(count % (10^9 +7))