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: Accepted)

def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
  
def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m
x, y = map(int, input().split())
inf = 10**9+7
if (x+y)%3 > 0:
  print(0)
else:
  n = (x+y)//3
  c = [1 for i in range(n+1)]
  invc = [1 for i in range(n+1)]
  for i in range(1, n+1):
    c[i] = c[i-1]*i % inf
    invc[i] = modinv(c[i], inf)
  cnt=-1
  for i in range(n+1):
    if (i+2*(n-i)==x)&(2*i+(n-i)==y):
      cnt = i
      break
  if cnt < 0:
    ans = 0
  else:
    ans = (c[n] * invc[cnt] * invc[n-cnt]) % inf
  print(ans)