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 math

def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
X,Y = map(int,input().split(' '))

if (X+Y)%3 == 0:
    if X > Y:
        diff = X - Y
        all_num = (X+Y)//3
        count_2 = all_num//2 + diff//2
    elif Y > X:
        diff = Y - X
        all_num = (X+Y)//3
        count_2 = all_num//2 + diff//2
    else:
        all_num = (X+Y)//3
        count_2 = all_num//2 
    print(combinations_count(all_num,count_2)%((10**9) + 7))
else:
    print(0)