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 fact(n)
  return 1 if n == 1
  return (1..n).inject(1){|r,a|r*a}
end
X, Y = gets.chomp.split(" ").map(&:to_i)
m = (2*Y - X)%3==0 ? (2*Y - X)/3 : nil 
n = (2*X - Y)%3==0 ? (2*X - Y)/3 : nil
if m && n
  puts (fact(m+n)/(fact(m)*fact(n))) % (10**9 + 7)
else
  puts 0
end