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: Runtime Error)

x,y=map(int,input().split())
mod = 10**9+7
flflag=True

if (2*x-y)%3==0:
  a=(2*x-y)//3
else:
  flflag=False
if (2*y-x)%3==0:
  b=(2*y-x)//3
else:
  flflag=False

def kaijou(n):
  ans = 1
  for i in range(1,n+1):
    ans*=i%mod
    ans%=mod  
  return ans

N=a+b
R=min(a,b)
ans=0
if a>=0 and b>=0 and flflag==True:
  ans=kaijou(N)
  ans1= (kaijou(N-R)*kaijou(R))%mod
  print((ans*pow(ans1,mod-2,mod))%mod)
else:
  print(0)