# Paths on a Grid

Imagine you are attending your math lesson at school.
Once again, you are bored because your teacher tells
things that you already mastered years ago
(this time he's explaining that
*(a+b)*^{2}=a^{2}+2ab+b^{2}).
So you decide to waste your time with drawing modern art instead.

Fortunately you have a piece of squared paper and you
choose a rectangle of size *n×m* on the paper.
Let's call this rectangle together with the lines it
contains a grid. Starting at the lower left corner of
the grid, you move your pencil to the upper right corner,
taking care that it stays on the lines and moves only to
the right or up. The result is shown on the left:

Really a masterpiece, isn't it?
Repeating the procedure one more time, you arrive with
the picture shown on the right.
Now you wonder: how many different works of art can you produce?

**Input Specification**

The input contains several test cases. Each is specified
by two unsigned 32-bit integers *n* and *m*,
denoting the size of the rectangle. As you can observe,
the number of lines of the corresponding grid is one
more in each dimension.
Input is terminated by *n* and *m=0*.
*Rectangles of width or height of 0 (but not both) are permitted.*

**Output Specification**

For each test case output on a line the number of
different art works that can be generated using the
procedure described above. That is, how many paths
are there on a grid where each step of the path
consists of moving one unit to the right or one unit up?
You may safely assume that this number fits into a
32-bit unsigned integer.

**Sample Input**

5 4
1 1
0 0

**Sample Output**

126
2

*All input is on the standard input stream; write all output
to the standard output stream.
*
## Turning it in

The submit project tag for this assignment is `grid`.
For your convenience, here is a submission form for this assignment.