**MathemagiclandInput: **standard input

Output:

Time Limit:

Jack
has been abducted by a man in black suit to Mathemagicland.
Fortunately, he met a friend Donald Duck. Donald Duck will help him
escape only if he first finds all * n*-tuple solutions:

after
Donald Duck gives Jack n rational values

where

are
called the elementary symmetric polynomials.

For
example: if n=1, then

If
n=2, then

If
n=3, then

If
n=4, then

However,
since most irrational numbers are impossible to represent exactly using a computer, you are only required to output the rational components of in numerical order.

**Input**

There are less than **1001** test cases.
For each test case, the first line contains two integers **n **and**
k, ** **n>0, |k|>0,
n<101, |k|<1001.**

The second line contains **n** integers
separated by a single space,

After
the last test case, a single integer of 0 is given.__Output__

Each
* n*-tuple solution should be outputted in exactly one line and in the
form of:

Such that

Two
* n*-tuple solutions are said to be the same if they have the same
output. Two solutions are said to be distinct if they are not the
same. Output all distinct solutions in lexicographical order, one in
each line. If there is no solution
(ie there are no rational elements in any of the valid n-tuples x

**
Note: All inputs/outputs will fit into a standard 32-bit signed integer.**

__Sample
Input__

2 1

2 1

0__Sample
Output__

1 1

**Problem
setter: Yin Zhao (aka Bugz Podder)**

"**~~
A man in a black suit will come and take you away at 1:42...and you
will be abducted to Mathemagicland (where you will meet Donald Duck).
~~**"