# Recurs

Time Limit: 2 Seconds Memory Limit: 65536 KB

Consider the recursive relation *f _{n}* =

*af*+

_{n-1}*bf*.

_{n-2}Given *f _{0}*,

*f*,

_{1}*n*and

*X*, you must find positive integers

*a*and

*b*such that

*f*=

_{n}*X*.

## Input

There are multiple test cases in the input. Each test case is a line with four integers *f _{0}*,

*f*,

_{1}*n*, and (1 <=

*f*,

_{0}*f*,

_{1}*X*<= 10

^{9}and 4 <=

*n*<= 10

^{9}). The input terminates with a line of the form "0 0 0 0" (without quotation marks) which should not be processed as a test case.

## Output

For each test case, write a single line containing the two required integers *a* and *b*. If there are
multiple solutions, write the one with the minimum value of *a*. If there is no solution, print "No solution" (without quotation marks).

## Sample Input

1 2 4 29 1 2 4 7 0 0 0 0

## Sample Output

2 1 No solutionSubmit

Source: 9th Iran Nationwide Internet Contest