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)

#145_D
x,y=map(int,input().split())
mod=10**9+7
if (x+y)%3!=0:
    print(0)
else:
    n=(2*x-y)//3
    m=(2*y-x)//3
    if n<0 or m<0:
        print(0)
    else:
        f=[1 for i in range(m+n+1)]
        for i in range(2,m+n+1):
            f[i]=f[i-1]*i%mod
        print(f[m+n]*pow(f[n],mod-2,mod)*pow(f[m],mod-2,mod)%mod)