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
 
def fac(n, m)
    (n..m).inject(1) {|r, v| r * v % $mod}
end
 
def power(x, n)
    n == 0 ? 1 : ((n.odd? ? x : 1) * power(x ** 2 % $mod, n / 2) % $mod)
end
 
def com(n, m)
    m = n - m if n < 2 * m
    fac(n - m + 1, n) * power(fac(1, m), $mod - 2) % $mod
end


x, y = gets.split.map(&:to_i)
 
a, ma = (2 * y - x).divmod(3)
b, mb = (2 * x - y).divmod(3)
 
puts a < 0 || b < 0 || ma != 0 || mb != 0 ? 0 : com(a + b, a)