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)

input = gets.chomp.split(" ").map(&:to_i)
X = input[0]
Y = input[1]
modu = 10 ** 9 + 7

inverses = []

def derive_inverse(m, modu, inverses=[])
  (1..m).each do |num|
    i = 0
    res = 1
    while !(res % num == 0) do
      res += modu
      i += 1
    end
    inv = (1 + i * modu) / num
    inverses << inv
  end
end


if (2 * Y - X) % 3 == 0 && (2 * X - Y) % 3 == 0
  m = (2 * Y - X) / 3
  n = (2 * X - Y) / 3 
  answer = 1
  derive_inverse(m,modu,inverses)
  m.times do |i|
    answer = ((answer * (n + 1 + i) ) % (10 **9 + 7) )* inverses[i]
  end
else
  answer = 0
end

puts answer % modu