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 (3.4.3) (judge verdict: Accepted)

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

mod=10**9+7
n=10**6
f=[1,1]
g=[1,1]
h=[0,1]

for i in range(2,n+1):
  f.append(f[-1]*i%mod)
  h.append((-h[mod%i]*(mod//i))%mod)
  g.append(g[-1]*h[i]%mod)
  
def cmb(n,r):
  p=f[n]*g[r]*g[n-r]%mod
  return p

if x==y:
  if x%3==0:
    print(cmb((x+y)//3,x//3))
  else:
    print(0)
elif x>y:
  if 2*y-x>=0 and (2*y-x)%3==0:
    print(cmb((x+y)//3,(2*y-x)//3))
  else:
    print(0)
else:
  if 2*x-y>=0 and (2*x-y)%3==0:
    print(cmb((x+y)//3,(2*x-y)//3))
  else:
    print(0)