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: Time Limit Exceeded)

def kCr(k, r)
  u = 1
  for i in 0..(r-1)
    u *= k-i
    u %= (10**9+7)
  end
  d = 1
  for i in 1..r
    d *= i
    d %= (10**9+7)
  end
  
  while u < d || u % d != 0
      u += 10**9+7
  end
  return u/d
end

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

yoko = 0
for i in 0..(x/2)
  if 2*(x - 2*i) == (y - i)
    yoko = i
    break
  end
  yoko = -1 if i == x/2
end

if yoko == -1
  puts 0
else
  tate = x - 2*yoko
  ans = kCr(yoko+tate, [yoko,tate].min)
  puts ans % (10**9+7)
end