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)

X,Y = gets.split.map &:to_i
A3 = 2*X - Y
B3 = 2*Y - X
unless A3 >= 0 && B3 >= 0 && A3 % 3 == 0 && B3 % 3 == 0
  p 0; exit
end

A = A3 / 3; B = B3 / 3;

Mod = 10**9+7

def powmod(b,r,mod)
  a = 1
  while r > 0
    if r%2 == 1
      a = a * b % mod
    end
    b = b * b % mod
    r /= 2
  end
  a
end

def invmod(f, mod)
  powmod(f, mod-2, mod)
end

def factorial(n, mod)
  fs = [1]
  (1..n).each{ |k| fs << (fs[-1] * k) % mod }
  fs
end

$fs = factorial(A+B,Mod)

def comb(n,r)
  return 0 if r < 0
  return 0 if n < r
  $fs[n] * invmod($fs[r],Mod) % Mod * invmod($fs[n-r],Mod) % Mod
end

p comb(A+B, A)