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Problem 1052. -- The Stern-Brocot Number System ## The Stern-Brocot Number System

Time Limit: 1 Sec Memory Limit: 64 MB

Submit: 19 Solved: 11

[Submit][Status][Discuss]## Description

The *Stern-Brocot tree* is a beautiful way for constructing the set of
all non-negative fractions where *m*
and *n* are relatively prime. The idea is to start with two fractions
,
and then repeat the following operation as many times as desired:

Insert
between two adjacent fractions
and
.

For example, the first step gives us one new entry between
and
,

and the next gives two more:

The next gives four more:

The entire array can be regarded as
an infinite binary tree structure whose top levels look like this-

This construction preserves order, and thus we cannot possibly get the same
fraction in two different places.

We can, in fact, regard the *Stern-Brocot tree* as a *number system* for
representing rational numbers,
because each positive, reduced fraction occurs exactly once. Let us use
the letters ```L`'' and ```R`'' to stand for going
down the left or right branch as we proceed from the root of the tree
to a particular fraction; then a string
of `L`'s and `R`'s uniquely identifies a place in the tree.
For example, `LRRL` means that we go left from
down to
, then right to
,
then right to
, then left to
.
We can consider LRRL to be a
representation of
. Every positive fraction gets represented in this
way as a unique string of `L`'s and `R`'s.

Well, almost every fraction.
The fraction
corresponds to
the empty string.
We will denote it by *I*, since that looks something
like 1 and stands for ``identity."

In this problem, given a positive rational fraction,
represent it in the *Stern-Brocot number system*.

## Input

The input file contains multiple test cases. Each test case consists of a line containing two positive integers m and n, where m and n are relatively prime. The input terminates with a test case containing two 1's for m and n, and this case must not be processed.

## Output

For each test case in the input file, output a line containing the representation of the given fraction in the Stern-Brocot number system.

## Sample Input

5 7
878 323
1 1

## Sample Output

LRRL
RRLRRLRLLLLRLRRR

## HINT

## Source

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