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 (7.3.0) (judge verdict: Runtime Error)

od = 10**9+7
def comb(n, k):
    c = 1
    for i in range(k):
        c *= n - i
        c %= mod
    d = 1
    for i in range(1, k + 1):
        d *= i
        d %= mod
    return (c * pow(d, mod - 2, mod)) % mod
x,y=map(int,input().split())

ans=0

z=x//2+1

for q in range(z,x+1):
  w=2*q-x
  if w*2+(q-w)==y:
    t=comb(q,w)
    ans+=t
    
  
  
print(ans)