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=1000000007
def modinverse(a,m)
  b=m
  u=1
  v=0
  while b>0
    t=a/b
    a-=t*b
    u-=t*v
    a,b=b,a
    u,v=v,u
  end
  u%=m
  if u<0
    u+=m
  end
  return u
end
x,y=gets.split.map(&:to_i)
s=x+y
b=s/3
if s%3!=0||x<b||y<b
  puts 0
  exit
end
x-=b
y-=b
a=1
y.times do |i|
  a*=x+i+1
  a%=mod
  a*=modinverse(i+1,mod)
  a%=mod
end
puts a