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
N = 10 ** 6
n = (2 * y - x) / 3
m = (2 * x - y) / 3

$fact = [1, 1]
$factinv = [1, 1]
$inv = [0, 1]

def com(n, k, mod)
    return 0 if (k < 0) || (n < k)
    k = k > n-k ? n-k : k
    return $fact[n] * $factinv[k] * $factinv[n-k] % mod
end

(2..N).each do |i|
    $fact << ($fact[-1] * i) % mod
    $inv << ((-1) * $inv[mod % i] * (mod / i)) % mod
    $factinv << ($factinv[-1] * $inv[-1]) % mod
end

if n > 0 && m > 0 && (x+y) % 3 == 0 then
    puts com(n+m, n, mod) % mod
else
    puts 0
end