TREE  Another Counting Problem
Tree is an important data structure in Computer
Science. Of all trees we work with, Binary Tree is probably the most popular
one. A Binary Tree is called a Strictly Binary Tree if every nonleaf
node in a binary tree has nonempty left and right subtrees. Let us define a
Strictly Binary Tree of depth d, as a Strictly Binary Tree that has at
least one root to leaf path of length d, and no root to leaf path in
that tree is longer than d. So let us use a similar reasoning to
define a generalized structure.
An nary Tree is called a Strictly nary Tree if every nonleaf node in an nary tree has n children each. A Strictly nary Tree of depth d can now be defined as a Strictly nary Tree that has at least one root to leaf path of length d, and no root to leaf path in that tree is longer than d.
Given the value of n and depth d, your task is to find the number of different strictly nary trees of depth d.
The figure below shows the 3 different strictly binary trees of depth 2.
Input
Input consists of several test cases. Each test case consists of two integers n (0 < n <= 32), d (0 <= d <= 16). Input is terminated a test case where n=0 and d=0, you must not process this test case.
Output
For each test case, print three integers, n, d and the number of different strictly nary trees of level d, in a single line. There will be a single space in between two integers of a line. You can assume that you would not be asked about cases where you had to consider trees that may have more than 2^{10} nodes in a level of the tree. You may also find it useful to know that the answer for each test case will always fit in a 200 digit integer.
Example
Input: 2 0 2 1 2 2 2 3 3 5 0 0 Output: 2 0 1 2 1 1 2 2 3 2 3 21 3 5 58871587162270592645034001
hide comments
navin_jr07:
20151013 07:50:01
using the additional library for storing the output.. Its worked for me.. Last edit: 20170217 17:21:22 

Deepak Gupta:
20141214 16:57:54
Considering max number of nodes on a level to be 999999 worked for me. 

:D:
20110611 18:29:32
There ARE trees with levels bigger that 2^10. The general input constraints seem to hold. You can still assume that number of digits is at most 200 (info taken from the forum). 
Added by:  Nguyen Van Quang Huy 
Date:  20060214 
Time limit:  0.5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO 
Resource:  acm.uva.es 