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)

x,y = gets.chomp.split.collect{ |item| item.to_i}


modi = 1000000007
result = 0
add = x+y
sub = -1
base = add/3

min = base*2 + 1
if x>y
  sub = x - 2*y
  oneA = min - x
else
  sub = y - 2*x
  oneA = min - y
end


def combi(n,k)
  return 0 if k < 0 || n < k
  return 1 if k == 0
  bunsi = 1
  bunbo = 1
  kk = ((n-k) < k) ? n-k : k
  kk.times do |ki|
    bunsi *= (n-ki)
    bunsi = bunsi / (ki+1)
  end
  return bunsi
end


if (add%3 ==0) && (sub <= 0)
  oneA -=1
  ans = combi(base,oneA)
  puts ans % modi

else
  puts 0
end