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 (3.4.3) (judge verdict: Accepted)

def com(N,K,mod):
    n=N
    K=min(K,N-K)
    k=K
    X=1  #分子
    Y=1  #分母
    for _ in range(K):
        X*=n
        X%=mod
        n-=1
    for _ in range(K):
        Y*=k
        Y%=mod
        k-=1
    Y=loop_pow(Y,mod-2,mod)  #Y**(mod-2) mod(mod)
    return X*Y%mod  #nCk mod(mod)

def loop_pow(x,n,mod):
    if n==0:
        return 1
    if n%2==0:
        t=loop_pow(x,n//2,mod)
        return (t*t)%mod
    return x*loop_pow(x,n-1,mod)%mod

def main():
    X,Y=map(int,input().split())
    if (X+Y)%3!=0:
        print(0)
    else:
        n=(2*Y-X)//3
        m=(2*X-Y)//3
        if n<0 or m<0:
            print(0)
        else:
            mod=10**9+7
            print(com(n+m,n,mod))

if __name__=="__main__":
    main()