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: Runtime Error)

from math import factorial
X, Y = map(int,input().split())

MOD = 10**9+7


if (X+Y)%3 != 0:
    ans = 0
else:
    N = int((X+Y)/3)

    if X >= Y:
        #K = N - (X - Y) + 1
        K = N/2 - (X - Y) + 1

    else:
        K = N/2 + (Y - X) + 1

    #ans = factorial(N-1)/(factorial(N-K)*factorial(K-1))
    # ans = factorial(N+1-1)/(factorial(N-K+1)*factorial(K-1))
    # ans %= MOD
    bunsi = factorial(N)%MOD
    bunbo = (factorial(N-K+1)*factorial(K-1))%MOD
    ans = int(bunsi/bunbo)


#print(N)
#print(K)
print(ans)