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 (3.8.2) (judge verdict: Wrong Answer)

#!/usr/bin/env python
# coding: utf-8

# In[8]:


def nCk(n, k, mod):
    a = 1
    for i in range(n, n-k, -1):
        a *= i
        a %= mod
    b = 1
    for i in range(1, k+1):
        b *= i
        b %= mod
    a *= pow(b, mod-2, mod)
    return a


# In[1]:


x,y = map(int,input().split())


# In[11]:


mod = 10**9+7
if (x+y)%3 != 0:
    ans = 0
else:
    right = x - (x+y)//3
    up = y - (x+y)//3
    if right < 0 or up < 0:
        ans = 0
    else:
        ans = nCk(right+up,right,mod)
print(ans)


# In[ ]: