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: Runtime Error)


if __name__ == "__main__":
  law = 10 ** 9 + 7
  
  dest_x, dest_y = sorted(map(int, input().split()), reverse=True)
  W = H = dest_x + 1
  
  num_pattern = [[0] * W for j in range(H)]
  
  num_pattern[0][0] = 1
  
  stack = [(0, 0, 0, 0)]
  moves = [(1, 2), (2, 1)]
  
  while(stack):
    x, y, or_x, or_y = stack.pop(0)
    
    for dx, dy in moves:
      if x + dx != or_x and y + dy != or_y and 0 <= x + dx < W and 0 <= y + dy < H and x + dx >= y + dy:
        num_pattern[x + dx][y + dy] += num_pattern[x][y]
        stack.append((x + dx, y + dy, x, y))
      
  print(num_pattern[dest_x][dest_y] * 2 % law)
  pass