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: Accepted)

p,q=map(int,input().split())
mod=10**9+7
x=(2*q-p)//3
y=q-2*x
def ie(n,r,mod):
  if r==1:
    return n%mod
  elif r%2==0:
    return (ie(n,r//2,mod)**2)%mod
  else:
    return ((ie(n,r//2,mod)**2)*n)%mod
if x+2*y!=p or 2*x+y!=q or x<0 or y<0:
  print(0)
elif x==0 or y==0:
  print(1)
else:
  a=[(x+y)%mod]
  b=[1]
  for i in range(1,min(x,y)):
    a.append(a[-1]*(x+y-i)%mod)
    b.append(b[-1]*(i+1)%mod)
  print((a[-1]*ie(b[-1],mod-2,mod))%mod)