You are about to organize a big programming competition. N competitors are registered for it. You know that you are going to divide all of them in some number of rooms. After the competition, each room will have its own leaderboard computed i.e. the order of competitors in that room based on their performance. You decided that after the competition, K random competitors will be awarded by lucky-one award. You will mark these lucky competitors with stars near their names on leaderboards. You set the scoring in such a way that there will be no draws between any players.

A global leaderboard is a set of leaderboards of all rooms after the competition, with exactly K lucky competitors marked with stars near their names.

You are interested in how many different global leaderboards exist.

Since the resulting number of global leaderboards can be very large, you are interested its value modulo 10⁹ + 7

Input:

In the one and only line of input, there are two integers N and K, denoting the number of competitors registered for the contest and the number of competitors to be awarded by lucky-one award.

Output:

In one line, output the number of different global leaderboards.

Constraints:

1 ≤ N ≤ 1000
0 ≤ K ≤ N