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)

x,y=map(int,input().split())
if (x+y)%3!=0:
  print(0)
else:
  n=(x+y)//3
  if x<n:
    print(0)
  else:
    def modinv(a, mod=10**9+7):
      return pow(a, mod-2, mod)
    def comb(n, r, mod=10**9+7):
      r = min(r, n-r)
      res = 1
      for i in range(r):
        res = res * (n - i) * modinv(i+1, mod) % mod
      return res 
    print(comb(n,x-n)%(10**9+7))