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)

# -*- coding: utf-8 -*-
x, y = map(int, input().split())

# 10 ** 9 + 7 is prime?

ans = 0
cnt = int((x + y) / 3)

if (x + y) % 3 != 0:
    ans = 0
elif x < cnt or x > 2 * cnt:
    ans = 0
else:
    m = int((2 * y - x) / 3) 
    n = cnt - m
    modulo = (10 ** 9) + 7
    fact = 1
    for i in range(1, n+1):
        fact = (fact * (m + i) / i) % modulo
    ans = int(fact)

print(ans)