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: Accepted)

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

A = (2*Y - X)/3
B = (2*X - Y)/3
if (2*Y - X) % 3 != 0 or (2*X - Y) % 3 != 0 or A < 0 or B < 0:
    ans = 0
    print(ans)
else:
    A = int(A)
    B = int(B)
    p = 10**9 + 7
    def comb(n, r, p):
        num1, num2 = 1, 1
        for i in range(r):
            num1 *= n-i
            num2 *= i+1
            num1 %= p
            num2 %= p
        return int(num1 * pow(num2, p-2, p))
    ans = comb(A+B, A, p)
    print(ans % p)