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 math

X, Y = map(int, input().split())
mod = 1000000007

if (X+Y) % 3 != 0 or X < 3 or Y < 3:
  print(0)
  exit()

# t=X方向に+1する回数(=Y方向に+2する回数)を仮にXと同じ値にする
t = X

# tを調整
while(t * 2 > Y):
  t -= 1
#print(t)

# r=総移動回数
r = t + (X-t)//2
#print(r)

ans = math.factorial(r) % mod
print(ans)