p02862 AtCoder Beginner Contest 145 - Knight
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.

Examples

Input

3 3


Output

2


Input

2 2


Output

0


Input

999999 999999


Output

151840682
```python
X,Y = map(int, input().split())
m = (-X+2*Y)//3
n = (2*X-Y)//3

def combination(n, r, mod=10**9+7):
    n1, r = n+1, min(r, n-r)
    numer = denom = 1
    for i in range(1, r+1):
        numer = (numer*(n1-i)) % mod
        denom = (denom*i) % mod
    return numer * pow(denom, mod-2, mod) % mod

if (X+Y)%3 != 0 or m*n<0:
  print(0)
else:
  print(combination(m+n,n))
```