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: Wrong Answer)

X,Y = list(map(int,input().split()))

n = (-X+2*Y)//3
m = (2*X-Y)//3
MOD = 10**9+7
 
def comb(n,r,MOD):
    x = n+1
    y = min(r,n-r)
    
    numer = 1
    denom = 1
    
    for i in range(1,r+1):
        numer = numer*(x-i)%MOD
        denom = denom*(i)%MOD
    
    return numer * pow(denom,MOD-2,MOD) % MOD
  
if (-X+2*Y)%3 == 0 and (2*X-Y)%3 == 0:
    print(comb(n+m,n,MOD))
else:
    print(0)