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)

x,y=gets.strip.split.map(&:to_i)
if(x+y)%3!=0
  p 0;exit
end

k=x-(x+y)/3
l=y-(x+y)/3

MOD = 10**9+7
 
def power(x, n)
  return 1 if n.zero?
 
  if n.even?
    return power(x*x, n/2) % MOD
  else
    return x*power(x, n/2)**2 % MOD
  end
end

$fac = []
$fac[0] = $fac[1] = 1
2.upto(k+l) do |num|
  $fac[num] = num * $fac[num-1] % MOD
end

$ifac = []
$ifac[0] = $ifac[1] = 1
$ifac[k+l] = power($fac[k+l], (MOD-2)) % MOD
(k+l-1).downto(2) do |num|
  $ifac[num] = $ifac[num+1] * (num+1) % MOD
end

def comb(n,k)
  return 0 if n<k || n<0 || k<0
  $fac[n] * ($ifac[n-k] * $ifac[k] % MOD) % MOD
end

p comb(k+l,k)