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: Accepted)

mod = 10**9+7

def pow(n, x):
  if x == 0:
    return 1
  elif x % 2 == 0:
    return pow(n * n % mod, x // 2)
  else:
    return n * pow(n * n % mod, x // 2) % mod

def comb(n, r):
  p, q = 1, 1
  for i in range(r):
    p = p * (n-i) % mod
    q = q * (i+1) % mod
  return p * pow(q, mod-2) % mod

x, y = map(int, input().split())
m = abs(x - y)
n = (x + y) // 3
if (x + y) % 3 == 0 and n >= m:
  print(comb(n, (n + m) // 2))
else:
  print(0)