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: Time Limit Exceeded)

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

from math import factorial 
P = int(1e9)+7
def c(n, m, P):
       ch = 1
       for i in range(m):
           ch *= (n-i)
           ch %= P
       b = factorial(m) 
       b = pow(b, P-2, P)
       return ch*b%P
def main():
    x, y = map(int, readline().split())
    a = 2*y-x
    b = 2*x-y
    if (a%3) or (b%3):
        print(0)
        return
    a = a//3
    b = b//3
    if a < 0:
        print(0)
        return
    if b < 0:
        print(0)
        return
    print(c(a+b, a, P)) 
if __name__ == '__main__':
    main()