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: Runtime Error)

x, y = gets.split.map(&:to_i)
if ((x + y) % 3 != 0) || (x < y/2) || (y < x/2) then
  puts 0
else
  x, y = [x, y].sort
  k3 = (x + y) / 3
  x -= k3
  y -= k3 * 2
  k1 = x
  k1 = k3 - k1 if k1 > k3 / 2
  k2 = k3 - k1 + 1
  puts ( ( k2.upto(k3).inject(:*) ) / ( 1.upto(k1).inject(:*) ) ) % (10**9 + 7)
end