Mathemagicland
Input: standard input
Output: standard output
Time Limit: 1 second

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 x1,x2,...,xn) , output “No solution.” without quotes. Print a blank line between each test case.

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). ~~"