Knight#12316

Knight

1 second
128 megabytes
Easy

There is a knight (the chess piece) placed at the origin of a two-dimensional grid.

From the square , the knight can move to either (i + 1, j + 2) or (i + 2, j + 1).

In how many different ways can the knight reach the square ?

Compute the number of such ways modulo 10^9 + 7.

Input

Two integers and (1 \le x, y \le 10^6).

Output

Print the number of ways the knight can reach the square modulo 10^9 + 7.

Examples

Example 1

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Example 2

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