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 (2.7.1) (judge verdict: Accepted)

x, y = gets.split.map(&:to_i)
mod = 10**9 + 7

def factorial(x, mod)
  return 1 if x == 0
  1.upto(x).inject { |i, j| i * j % mod }
end

def inv_fact(x, mod)
  factorial(x, mod).pow(mod - 2, mod)
end

def combination(x, y, mod)
  factorial(x, mod) * inv_fact(y, mod) * inv_fact(x - y, mod)
end

if (2 * x - y) % 3 == 0 && (-x + 2 * y) % 3 == 0
  u = (2 * x - y) / 3
  v = (-x + 2 * y) / 3

  if u >= 0 && v >= 0
    puts combination(u + v, u, mod) % mod
  else
    puts 0
  end
else
  puts 0
end