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 Ruby (2.3.3) (judge verdict: Wrong Answer)

X, Y = gets.chomp.split.map(&:to_i)

if (X + Y) % 3 != 0
  p 0
  exit
end

# n ->  +1, +2 の移動回数
# m ->  +2, +1 の移動回数

n = (2 * Y - X) / 3
m = (2 * X - Y) / 3

if n < 0 || m < 0
  p 0
  exit
end

def factorial(f,e)
  (f..e).inject(1) do |sum, a|
    (sum * a) % (10 ** 9 + 7)
  end
end

p ((factorial(m+1, n+m)) / (factorial(1,n))) % (10 ** 9 + 7)