A full set

Alex is still bored. To amuse himself, he took N dices, numbered from 1 to N, shuffled them, took K of them randomly and then recorded their numbers and returned them to the pile. Then he repeated these steps: shuffle them again, again took the K dices, and so on. And now he has a question: how many times he need to do so, that each dice has been taken at least once?

Input

The single line contains two integers: N and K.

1 ≤ N ≤ 1000

1 ≤ K ≤ N

Output

You should print a single number — average number of iterations before each dice will be taken at least once. Output response should be with an absolute percentage error of no more than 10 ^7.

Examples