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: Runtime Error)

INF = float("inf") #const
MOD = 10**9+7 #const
MAX = 510000 #const

def repeat(n,p):
    if p == 0:
        return 1
    if p%2==0:
        t = repeat(n,p//2)
        return t * t % MOD
    return n * repeat(n,p-1) % MOD


def com(n,r):
    if n < r or n < 0:
        return 0
    if n == 0 and r == 0:
        return 1
    fact = [0] * (n+1)
    fact[0] = 1
    for i in range(n):
        fact[i+1] = fact[i] * (i+1) % MOD #階乗計算
    f_inv = repeat(fact[r],MOD-2)
    f = repeat(fact[n-r],MOD-2)

    return fact[n] * f_inv * f % MOD


def main():
    x,y = map(int,input().split())
    if (x+y)%3 != 0:
        print(0)
        return
    n = (2*y - x)//3
    m = (2*x - y)//3
    print(com(n+m,n))


if __name__ == "__main__":
    main()