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 (2.7.1) (judge verdict: Runtime Error)

g = gets.chomp.split(' ').map(&:to_i)

# g[0] = i + 2j
# g[1] = 2i + j
i = (2 * g[1] - g[0]) / 3
j = (2 * g[0] - g[1]) / 3
num = i+j
if num == 0
  puts 0
else
  a = (i < j) ? j : i
  numerator = [*(a+1..num)].inject(:*)
  denominator = [*(1..a)].inject(:*)
  puts (numerator / denominator) % ((10 ** 9) + 7)
end