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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

X,Y=map(int,input().split())
s=(2*X-Y)/3
u=(2*Y-X)/3
m=10**9+7  
def fact(n,p):
  ans=1
  for i in range(1,n+1):
      ans=ans*i%p
  return ans
def cal(x,a,p):
  ans=x%p
  memo=1
  while True:
    if a==1:break
    if a%2==0:
      ans=(ans*ans)%p
      a=a//2
    else:
      a=a-1
      memo=memo*ans
  return (ans*memo)%p
  
if s.is_integer() and u.is_integer():
  s=int(s)
  u=int(u)
  n=s+u
  ans=1
  ans=fact(n,m)
  s=fact(s,m)
  u=fact(u,m)
  s=cal(s,m-2,m)
  u=cal(u,m-2,m)
  ans=(ans*s*u)%m 
else:
  ans=0
print(ans)