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)

import sys
import numpy as np

INPUT = lambda: sys.stdin.readline().rstrip()
MAP = lambda: map(int, INPUT().split())

sys.setrecursionlimit(10 ** 9)
mod = 10 ** 9 + 7


def main():
    X, Y = MAP()
    if (X + Y) % 3 != 0:
        print(0)
        sys.exit()

    s = (2*X - Y)//3
    t = (2*Y - X)//3
    MAX_NUM = max(X, Y)
    dp = np.zeros((X+1, Y+1), np.int)
    for i in range(MAX_NUM):
        if i == 0:
            for j in range(len(dp[0])):
                if j == 0: dp[i][j] = 0
                else: dp[i][j] = 1
        else:
            for j in range(len(dp[0]-1)):
                if j == 0: dp[i][j] = 1
                else: dp[i][j] = dp[i-1][j] + dp[i][j-1]

    print(dp[s][t] % mod)


if __name__ == '__main__':
    main()