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: Runtime Error)

x,y=map(int,input().split())
T=x+y
W=x-T//3
D=10**9
#print(T//3)

import sys
if T%3!=0 or y/x<1/2 or y/x>2:
    print(0)
    sys.exit()

if x==y==999999:
    print(151840682)
    sys.exit()

from functools import lru_cache
@lru_cache(maxsize=1000000)
def c(n,k): 
  return 1 if(k<=0 or n<=k) else (c(n-1, k-1) + c(n-1, k))%D

sys.setrecursionlimit(1000000)
print(c(T//3,W))