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: Time Limit Exceeded)

from collections import deque

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

mod = 10**9 + 7

stack = deque([(0, 0)])


def dfs(stack):
    ans = 0
    while len(stack) > 0:
        x, y = stack.pop()
        if x == X and y == Y:
            ans += 1
            ans %= mod
        for i, j in ((2, 1), (1, 2)):
            new_x, new_y = x+i, y+j
            if new_x > X or new_y > Y:
                continue
            stack.append((new_x, new_y))

    return ans


ans = dfs(stack)
print(ans)