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: Wrong Answer)

import sys
input = sys.stdin.readline
from math import factorial
large_p = 10**9 + 7

def comb_mod(n, r, large_p):
    a, b = 1, 1
    r = min(r, n - r)
    for i in range(r):
        a = a * (n - i) % large_p
        b = b * (r - i) % large_p
    return a * pow(b, large_p - 2, large_p) % large_p

def main():
    x, y = map(int, input().split())
    p1, p2 = 0, 0

    for i1 in range(1, x//2 + 1):
        if x - i1 == (y - i1 * 2) * 2:
            p1 = i1
            p2 = y - i1 * 2
            break
    r = comb_mod(p1 + p2, p1, large_p)
    print(r)

if __name__ == '__main__':
    main()