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: Accepted)

from math import factorial as fac
x,y=map(int,input().split())
a=(2*y-x)/3
b=(2*x-y)/3
mod=10**9+7
if a>=0 and b>=0 and a==int(a) and b==int(b):
  a=int(a)
  b=int(b)
  a1=1
  a2=1  
  n3=10**9+7
  for i in range(a):
    a1*=a+b-i
    a2*=i+1
    a1%=n3
    a2%=n3
  a2=pow(a2,n3-2,n3)
  print((a1*a2)%n3)
else:
  print(0)