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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

X Y

outputFormat

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

样例

999999 999999

151840682