Problem F
Pascal's HyperPyramids
We programmers know and love Pascal’s triangle: an array of numbers with $1$ at the top and whose entries are the sum of the two numbers directly above (except numbers at both ends, which are always $1$). For programming this generation rule, the triangle is best represented leftaligned; then the numbers on the left column and on the top row equal $1$ and every other is the sum of the numbers immediately above and to its left. The numbers highlighted in bold correspond to the base of Pascal’s triangle of height $5$:
\[ \begin{array}{rrrrr} \hline 1 & 1 & 1 & 1 & \textbf{1}\\ 1 & 2 & 3 & \textbf{4} \\ 1 & 3 & \textbf{6} \\ 1 & \textbf{4} \\ \textbf{1} \end{array} \]Pascal’s hyperpyramids generalize the triangle to higher dimensions. In $3$ dimensions, the value at position $(x, y, z)$ is the sum of up to three other values:

$(x, y, z1)$, the value immediately below it if we are not on the bottom face ($z=0$);

$(x, y1, z)$, the value immediately behind if we are not on the back face ($y=0$);

$(x1, y, z)$, the value immediately to the left if we are not on the leftmost face ($x=0$).
All values at the bottom, back, and leftmost faces are $1$.
The following figure depicts Pascal’s 3Dpyramid of height $5$ as a series of plane cuts obtained by fixing the value of the $z$ coordinate.
$z = 0$ 
$z = 1$ 
$z = 2$ 
$z = 3$ 
$z = 4$ 
\[ \begin{array}{rrrrr}
\hline 1 & 1 & 1 & 1 & \textbf{1} \\ 1
& 2 & 3 & \textbf{4} \\ 1 & 3 &
\textbf{6} \\ 1 & \textbf{4} \\ \textbf{1}
\end{array} \]

\[ \begin{array}{rrrr}
\hline 1 & 2 & 3 & \textbf{4} \\ 2 & 6
& \textbf{12} \\ 3 & \textbf{12} \\ \textbf{4}
\end{array} \]

\[ \begin{array}{rrr}
\hline 1 & 3 & \textbf{6} \\ 3 &
\textbf{12} \\ \textbf{6} & \end{array} \]

\[ \begin{array}{rr}
\hline 1 & \textbf{4} \\ \textbf{4} \\ \end{array}
\]

\[ \begin{array}{c}
\hline \textbf{1} \end{array} \]

For example, the number at position $x=1$, $y=2$, $z=1$ is the sum of the values at $(0, 2, 1)$, $(1, 1, 1)$ and $(1, 2, 0)$, namely, $6 + 3 + 3 = 12$. The base of the pyramid corresponds to a plane of positions such that $x+y+z = 4$ (highlighted in bold above).
The size of each layer grows quadratically with the height of the pyramid, but there are many repeated values due to symmetries: numbers at positions that are permutations of one another must be equal. For example, the numbers at positions $(0,1,2)$, $(1,2,0)$ and $(2,1,0)$ above are all equal to $3$.
Task
Write a program that, given the number of dimensions $D$ of the hyperspace and the height $H$ of a hyperpyramid, computes the set of numbers at the base.
Input
A single line with two positive integers: the number of dimensions, $D$, and the height of the hyperpyramid, $H$.
Constraints
$2$ 
$\leq $ 
$D$ 
$<$ 
$32$ 
Number of dimensions 
$1$ 
$\leq $ 
$H$ 
$<$ 
$32$ 
Height 
$D$ and $H$ are such that all numbers in the hyperpyramid are less than $2^{63}$. 
Output
The set of numbers at the base of the hyperpyramid, with no repetitions, one number per line, and in ascending order.
Sample Input 1  Sample Output 1 

2 5 
1 4 6 
Sample Input 2  Sample Output 2 

3 5 
1 4 6 12 