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)

t = input().rstrip().split(" ")
x = int(t[0])
y = int(t[1])
temp = {}
def get_num(x, y):
    res = 0
    if (x == 0) and (y == 0):
        res = 1
    elif (x <= 0) or (y == 0):
        res = 0
    elif (x, y) in temp:
        res = temp[(x, y)]
    else:
        res += get_num(x-1, y-2) % (1e9+7)
        res += get_num(x-2, y-1) % (1e9+7)
        temp[(x, y)] = res
    return res

print(int(get_num(x, y)))