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: Accepted)

def rec(n, p, m)
  return 1 if p == 0
  if p % 2 == 0
    tmp = rec(n, p / 2, m)
    return tmp * tmp % m
  end
  n * rec(n, p - 1, m) % m
end
x, y = gets.chomp.split(' ').map(&:to_i)
xy = x + y
mod = (1e+9 + 7).to_i
if xy % 3 != 0
  puts 0
else
  n = xy / 3
  if !(x >= n && x <= 2 * n && y >= n && y <= 2 * n)
    puts 0
  else
    r = x - n
    arr = Array.new(n)
    arr[0] = 1
    (1...n).each do |i|
      arr[i] = arr[i - 1] * (i + 1) % mod
    end
    arr.unshift(1)
    a = arr[n]
    b = arr[n - r]
    c = arr[r]
    bc = (b * c) % mod
    puts (a * rec(bc, mod - 2, mod)) % mod
  end
end