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)

MOD = 10**9 + 7

def comb_inv(n, r)
  res = 1
  i = r
  j = 1
  while i > 0
    res = res * (n-i+1)
    res %= MOD
    j *= i
    j %= MOD
    i -= 1
  end
  res *= inv(j)
  res %= MOD
  res
end

def inv(x)
  res = 1 # 逆元をどんどんかけるやつ
  beki = x # 逆元を計算したい値のMOD化でのべき乗
  (MOD - 2).to_s(2).reverse.chars do |digest|
    res = (beki * res) % MOD if digest == '1'
    beki = (beki * beki) % MOD
  end
  res
end


if (x + y) % 3 != 0
  puts 0
  exit
end


q = (x+y) / 3

r = x % q

p comb_inv(q, r)