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)

MOD = (10**9) + 7
ONE = '1'.freeze

def nCk(n, k)
  (fact(k + 1, n) * inv(fact(1, n - k) % MOD)) % MOD
end

def fact(s, e)
  (s..e).reduce(1) { |r, i| (r * i) % MOD }
end

def inv(x)
  res = 1
  beki = x
  (MOD - 2).to_s(2).reverse.chars do |digest|
    res = (beki * res) % MOD if digest == ONE
    beki = (beki * beki) % MOD
  end
  res
end

x, y = gets.chomp.split.map(&:to_i)

min, max = [x, y].sort

# min,maxのdiff回多く片方の遷移をしている。
diff = max - min
d_min = min - diff
if !(d_min >= 0 && d_min == max - 2 * diff && (d_min % 3).zero?)
  puts 0
else
  a = b = d_min / 3
  a += diff
  puts nCk(a + b, b)
end