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: Runtime Error)

import sys
import math
sys.setrecursionlimit(200000)
MOD = 10 ** 9 + 7


def main():
    X, Y = map(int, input().split())
    while X != Y and X >= 0 and Y >= 0:
        if X > Y:
            X -= 2
            Y -= 1
        else:
            X -= 1
            Y -= 2
    if X % 2 == 1 and Y % 2 == 1:
        ab = math.factorial((X + Y) // 3)
        a = math.factorial(X // 3)
        b = math.factorial(Y // 3)
        print(ab // (a * b) % MOD)
    else:
        print(0)



if __name__ == "__main__":
    main()