Background

This problem is somewhat easier than the problem A Very Easy Problem! because of the super long time limit...

Description

Assurance Company of Moving (ACM) is a company of moving things for people. Recently, some schools want to move their computers to another place. So they ask ACM to help them. One school reserves K trucks for moving, and it has N computers to move. In order not to waste the trucks, the school ask ACM to use all the trucks. That is to say, there must be some computers in each truck, and there are no empty trucks. ACM wants to know how many partition schemes exists with moving N computers by K trucks, the ACM ask you to compute the number of different schemes with given N and K. You needn't care with the order. For example N = 7,K = 3, the the following 3 partition instances are regarded as the same one and should be counted as one scheme: "1 1 5","1 5 1","5 1 1". Each truck can carry almost unlimited computers!!

Input

Each line of the input contains two positive integer N (1 ≤ N ≤ 5000) and K (1 ≤ K ≤ N).Input is terminated by a line with N = K = 0 (this case should not be processed).

Output

For each line, output the number of different partition scheme. To avoid big integers, you must output the answer modulo 1988.

Example

Input:
1 1
7 3
0 0

Output:
1
4