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)

import sys
import threading
sys.setrecursionlimit(10**9)
threading.stack_size(128*1024*1024)
x, y = map(int, input().split())
MOD = 10**9+7
cnt = 0

def move(i, j):
    if i > x or j > y:
        return 0

    if i == x and j == y:
        return 1
    else:
        cnt =  ( move(i+1, j+2) ) % MOD + ( move(i+2, j+1) ) % MOD
        return cnt

if (x+y) % 3 != 0:
    print(0)
    sys.exit()
print(move(0, 0))