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 (7.3.0) (judge verdict: Time Limit Exceeded)

x, y = map(int, input().split())
r1 = 0
r2 = 0

def factorial(n):
    if n == 0:
        return 1
    else:
        a = 1
        for i in range(n):
            a *= n - i
        return a

def comb(a, b):
    return factorial(a) // (factorial(b) * factorial(a - b))

if y < x:
    temp = y
    y = x
    x = temp

dif = x - y
if ((y - dif) % 3 != 0) | (dif > y):
    print('0')
else:
    k = (y - dif) // 3
    n = comb(2 * k + dif, k) % (10**9 + 7)
    print(n)