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 Python (3.4.3) (judge verdict: Wrong Answer)

def ext_gcd(p, a):
  #require a, m be relative prime
  #m > a  
  if a == 0:
    return 1, 0
  else:
    x1, y1 = ext_gcd(a, p%a)
    y = x1 - y1 * int(p/a)
    x = y1
    return x, y

x, y = map(int, input().split())

n = int((2 * y - x)/3)
m = int((2 * x - y)/3)

if n != int(n) or m != int(m) or n<0 or m<0:
  ans = 0
else:
   n = int(n)
   m = int(m)
   if n < m :
      c = m
      m = n
      n = c
   # (n+m!)/(n!)(m!) mod (1e9+7)
   ans = 1
   prime = 1000000007 
   for i in range(n+1,m+n+1):
        ans = int(ans * i) 
        ans = (ans % prime)
   for i in range(1, m+1):
      ori_inv = int(ext_gcd(prime, i)[1])
      while ori_inv < 0 :
        ori_inv += prime
      ans = int(ans * ori_inv)  
      ans = (ans % prime)
print(ans)