COUNT  Another Very Easy Problem! WOW!!!
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 shemes exists with moving N computers by K trucks, the ACM ask you to compute the number of different shemes 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 sheme: "1 1 5","1 5 1","5 1 1". Each truck can carry almost unlimited computers!!
Input
Each line of the input contains two postisive 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 sheme. To avoid big integers, you may output the answer modudo 1988.
Example
Input:
1 1
7 3
0 0
Output:
1
4
hide comments
babur:
20170901 09:29:23
Classical Dp...learnt so much from this question


kshubham02:
20170824 07:49:59
@nap11, possibilities are  1,1,5; 1,2,4; 1,3,3; and 2,2,3. 

studyfather:
20170722 14:12:16
AC in one go!


hamjosh1:
20161116 19:29:34
solved in both top down and bottom up :D 

Bhuvnesh Jain:
20160112 22:45:46
1d dp solution with O(n^2) Last edit: 20160112 22:46:13 

Utkarsh Agarwal:
20151209 00:04:04
Too harsh for python codes. C++ gets accepted in .92 sec. python is atleast 10 times slower than c/c++. 

xxbloodysantaxx:
20150709 21:58:55
Yet another nice DP problem 

nap11:
20150629 10:07:19
plz tell me how it will be 4 for n=7 and k=3?


Bharath Reddy:
20140914 13:42:55
Looking at the comments helped me arrive at the right algorithm :) Awesome problem though. Last edit: 20140914 13:43:11 

Ouditchya Sinha:
20130719 17:21:41
@Juan Martinez : I'm not sure about JAVA but try declaring the array globally, which worked for me in C++.

Added by:  Fudan University Problem Setters 
Date:  20071103 
Time limit:  10s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 C99 ERL JSRHINO OBJC SQLITE 
Resource:  Time limit: 1000 Years! Memory limit: 2000 GB! Acc%: 100%! 