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 (3.8.2) (judge verdict: Runtime Error)

import sys
from math import factorial
input = sys.stdin.readline


def log(*args):
    print(*args, file=sys.stderr)


def main():
    x, y = map(int, input().rstrip().split())
    # 全部 i + 1, j + 2が最初だったとする
    # a + 2b = x, 2a + b = y
    # =>
    # a = x - 2b
    # b = y - 2a
    # =>
    # b = y - 2x + 4b
    # 3b = 2x - y
    # b = (2x - y) / 3
    # a = (2y - x) / 3
    if (2 * x - y) % 3 != 0 or (2 * y - x) % 3 != 0:
        print(0)
        return
    a = (2 * x - y) // 3
    b = (2 * y - x) // 3
    # (a + b) C min(a, b)
    # => (a + b)! / (min(a, b) ! * (a + b - min(a, b)) !
    mod = 10**9 + 7
    ans = ((factorial(a + b) % mod) * pow(factorial(min(a, b)), mod - 2, mod)
           * pow(factorial(a + b - min(a, b)), mod - 2, mod)) % mod
    print(ans)


if __name__ == '__main__':
    main()