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 (3.8.2) (judge verdict: Wrong Answer)

import math
mod=10**9+7
def mul(a, b):
    return ((a % mod) * (b % mod)) % mod
def div(a, b):
    return mul(a, pow(b, mod-2,mod))
x,y=map(int,input().split())
x,y=min(x,y),max(x,y)
s=y-x

if 3*(x//3)+2*s!=y:
  print(0)
else:
  a=x//3
  b=x//3+s
  A=1
  B=1
  C=1
  for i in range(1,a+b+1):
    A*=i
    A%=mod
  for i in range(1,a+1):
    B*=i
    B%=mod
  for i in range(1,b+1):
    C*=i
    C%=mod
  print(div(A,mul(B,C)))