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())

def cnb(n,k,p):
  if k>n:
    return 0
  c,d=1,1
  for i in range(k+1,n+1):
    c = (c*i)%p
  for i in range(1,k+1):
    d = (d*i)%p
  return (c*pow(d,p-2,p))%p

p=10**9+7
if (X+Y)%3!=0 or X > 2*Y or Y > 2*X:
  print(0)
else:
  ab=(X+Y)//3
  a=(-X+2*Y)//3
  print(cnb(ab,a,p))