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: Wrong Answer)

#!/usr/bin/env python
# -*- coding: utf-8 -*-
x,y=[int(x) for x in input().split()]
mod=10**9+7
def inv(a,n,mod):
    result=1
    while n>0:
        if n & 1==1:
            result*=a
            result%=mod
        a=a*a%mod
        n >>=1
    return result%mod

if (2*x-y)%3 !=0 or (2*y-x)%3!=0:
    print(0)
else:
    # p+2q=x
    # 2p+q=y
    p=(2*y-x)//3
    q=(2*x-y)//3
    ans=1
    for i in range(q):
        ans*=(p+q-i)%mod
        ans%=mod
        ans*=inv(i+1,mod-2,mod)
        ans%=mod
    print(ans)