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: Accepted)

MOD = int(1e9+7)


def div(a, b):
    return a * pow(b, MOD-2, MOD) % MOD


def fact(x):
    prev = 1
    ret = 1
    for i in range(1, x+1):
        ret = (i * prev) % MOD
        prev = ret
    return ret


def main():
    X, Y = map(int, input().split())
    N = (X+Y)//3
    if (X+Y) % 3 != 0 or X < N or Y < N:
        print(0)
        return
    ans = div(div(fact(N), fact(X-N)), fact(N*2-X))
    print(ans)


if __name__ == "__main__":
    main()