Permutation

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

Permutation plays a very important role in Combinatorics.

For example, 1 2 3 4 5 and 1 3 5 4 2 are both 5-permutations.

As everyone's known, the number of n-permutations is n!.
 
According to their magnitude relatives, if we insert the symbols "<" or ">" between every pairs of consecutive numbers of a permutation, we can get the permutation with symbols.
 
For example, 1 2 3 4 5 can be changed to 1< 2< 3< 4< 5,

1 3 5 4 2 can be changed to 1< 3 < 5 > 4 > 2.
 
Now it's your task to calculate the number of n-permutations with k "<" symbols.

Maybe you don't like large numbers, so you should just give the result mod 2007.

Input

Input may contain multiple test cases. Each test case is a line contains two integers n and k. 0 < n <= 100 and 0 <= k <= 100.

The input will terminated by EOF.

Output

The nonnegative integer result mod 2007 on a line.

Sample Input

5 2

Sample Output

66

Hint

Source