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 fact(n)
  (1..n).inject(1){ |ans,x| ans*x % MOD }
end

def pow(n, k)
  ans = 1
  while k > 0
    ans = ans*n % MOD if k.odd?
    n = n*n % MOD
    k >>= 1
  end
  ans
end

def comb(n, k)
  fact(n) * pow(fact(n-k),MOD-2) % MOD * pow(fact(k),MOD-2) % MOD
end

x, y = gets.chomp.split.map(&:to_i)

sum = x+y
x -= sum/3
y -= sum/3

if sum%3 != 0 || x < 0 || y < 0
  puts(0)
  exit
end


puts(comb(x+y, x))